LMFDB - Embedded newform 22.12.c.a.15.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,12,Mod(3,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("22.3");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	22.c (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.9035499723$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 339028 x^{18} - 38195378 x^{17} + 220926638311 x^{16} - 35915431412664 x^{15} + \cdots + 11\!\cdots\!00 $ x^20 - 4x^19 + 339028x^18 - 38195378x^17 + 220926638311x^16 - 35915431412664x^15 + 115759899998314350x^14 - 27226928185171403384x^13 + 41831014975562739810959x^12 - 3879797201571793549516048x^11 + 3316840467475291520075063190x^10 + 1067427514312498593848752050628x^9 + 750967910898548932251904101148531x^8 + 228128795234897755949671367783663114x^7 + 90326787979451743483651549716111634592x^6 + 21775725237124771428874092537573760059528x^5 + 5115171268695044278298633768429412143699481x^4 + 644893842489460735970879339730837145914702280x^3 + 40307167403308519805773510178453296556136973760x^2 - 118703222270772703791843925527006368174467110400*x + 1158220182319374358886221767374591631314546790400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{4}\cdot 5\cdot 11^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			15.5
Root			$-197.297 - 607.218i$ of defining polynomial
Character	$\chi$	$=$	22.15
Dual form			22.12.c.a.3.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-25.8885 - 18.8091i) q^{2} +(201.415 - 619.892i) q^{3} +(316.433 + 973.882i) q^{4} +(932.620 - 677.588i) q^{5} +(-16874.0 + 12259.7i) q^{6} +(-16358.4 - 50346.1i) q^{7} +(10125.9 - 31164.2i) q^{8} +(-200383. - 145587. i) q^{9} +O(q^{10})$	\(q+(-25.8885 - 18.8091i) q^{2} +(201.415 - 619.892i) q^{3} +(316.433 + 973.882i) q^{4} +(932.620 - 677.588i) q^{5} +(-16874.0 + 12259.7i) q^{6} +(-16358.4 - 50346.1i) q^{7} +(10125.9 - 31164.2i) q^{8} +(-200383. - 145587. i) q^{9} -36889.0 q^{10} +(131656. - 517666. i) q^{11} +667436. q^{12} +(283981. + 206324. i) q^{13} +(-523470. + 1.61108e6i) q^{14} +(-232188. - 714600. i) q^{15} +(-848316. + 616338. i) q^{16} +(-1.28534e6 + 933855. i) q^{17} +(2.44926e6 + 7.53805e6i) q^{18} +(379520. - 1.16804e6i) q^{19} +(955003. + 693851. i) q^{20} -3.45040e7 q^{21} +(-1.31452e7 + 1.09253e7i) q^{22} -3.80447e7 q^{23} +(-1.72789e7 - 1.25539e7i) q^{24} +(-1.46781e7 + 4.51744e7i) q^{25} +(-3.47107e6 - 1.06829e7i) q^{26} +(-3.71964e7 + 2.70248e7i) q^{27} +(4.38548e7 - 3.18624e7i) q^{28} +(4.89155e7 + 1.50546e8i) q^{29} +(-7.43001e6 + 2.28672e7i) q^{30} +(1.37249e8 + 9.97173e7i) q^{31} +3.35544e7 q^{32} +(-2.94380e8 - 1.85878e8i) q^{33} +5.08406e7 q^{34} +(-4.93701e7 - 3.58695e7i) q^{35} +(7.83764e7 - 2.41218e8i) q^{36} +(-1.92238e8 - 5.91649e8i) q^{37} +(-3.17951e7 + 2.31005e7i) q^{38} +(1.85096e8 - 1.34480e8i) q^{39} +(-1.16729e7 - 3.59256e7i) q^{40} +(-1.13695e8 + 3.49917e8i) q^{41} +(8.93257e8 + 6.48989e8i) q^{42} -5.05494e6 q^{43} +(5.45806e8 - 3.55896e7i) q^{44} -2.85529e8 q^{45} +(9.84923e8 + 7.15588e8i) q^{46} +(6.56469e8 - 2.02040e9i) q^{47} +(2.11199e8 + 6.50004e8i) q^{48} +(-6.67440e8 + 4.84923e8i) q^{49} +(1.22969e9 - 8.93419e8i) q^{50} +(3.20002e8 + 9.84865e8i) q^{51} +(-1.11074e8 + 3.41851e8i) q^{52} +(4.41119e8 + 3.20492e8i) q^{53} +1.47127e9 q^{54} +(-2.27980e8 - 5.71995e8i) q^{55} -1.73464e9 q^{56} +(-6.47618e8 - 4.70522e8i) q^{57} +(1.56530e9 - 4.81749e9i) q^{58} +(-2.93263e9 - 9.02572e9i) q^{59} +(6.22464e8 - 4.52247e8i) q^{60} +(-1.00967e10 + 7.33571e9i) q^{61} +(-1.67758e9 - 5.16307e9i) q^{62} +(-4.05177e9 + 1.24701e10i) q^{63} +(-8.68675e8 - 6.31130e8i) q^{64} +4.04649e8 q^{65} +(4.12485e9 + 1.03491e10i) q^{66} -8.21768e8 q^{67} +(-1.31619e9 - 9.56268e8i) q^{68} +(-7.66278e9 + 2.35836e10i) q^{69} +(6.03447e8 + 1.85722e9i) q^{70} +(2.10989e10 - 1.53292e10i) q^{71} +(-6.56614e9 + 4.77058e9i) q^{72} +(-7.55965e9 - 2.32662e10i) q^{73} +(-6.15163e9 + 1.89328e10i) q^{74} +(2.50469e10 + 1.81976e10i) q^{75} +1.25763e9 q^{76} +(-2.82162e10 + 1.83985e9i) q^{77} -7.32134e9 q^{78} +(-2.01302e10 - 1.46254e10i) q^{79} +(-3.73534e8 + 1.14962e9i) q^{80} +(-4.29821e9 - 1.32285e10i) q^{81} +(9.52502e9 - 6.92033e9i) q^{82} +(2.15075e10 - 1.56261e10i) q^{83} +(-1.09182e10 - 3.36028e10i) q^{84} +(-5.65966e8 + 1.74187e9i) q^{85} +(1.30865e8 + 9.50789e7i) q^{86} +1.03175e11 q^{87} +(-1.47995e10 - 9.34477e9i) q^{88} +1.88613e10 q^{89} +(7.39193e9 + 5.37055e9i) q^{90} +(5.74213e9 - 1.76725e10i) q^{91} +(-1.20386e10 - 3.70511e10i) q^{92} +(8.94580e10 - 6.49950e10i) q^{93} +(-5.49970e10 + 3.99577e10i) q^{94} +(-4.37504e8 - 1.34650e9i) q^{95} +(6.75837e9 - 2.08001e10i) q^{96} +(9.34412e10 + 6.78890e10i) q^{97} +2.64000e10 q^{98} +(-1.01747e11 + 8.45641e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9}+O(q^{10}) $ 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9	\( 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9} - 354944 q^{10} - 449801 q^{11} + 108544 q^{12} + 3369596 q^{13} - 5349696 q^{14} + 12264628 q^{15} - 5242880 q^{16} + 1661262 q^{17} - 19177088 q^{18} + 49176291 q^{19} - 370688 q^{20} - 74218796 q^{21} - 5153632 q^{22} - 127653292 q^{23} - 3571712 q^{24} + 33758041 q^{25} - 99025728 q^{26} - 135657199 q^{27} + 156930048 q^{28} + 555960754 q^{29} + 392468096 q^{30} - 13977916 q^{31} + 671088640 q^{32} - 1768265081 q^{33} - 357119936 q^{34} + 584997860 q^{35} - 613666816 q^{36} - 161000626 q^{37} - 1456805888 q^{38} + 1145816470 q^{39} + 193593344 q^{40} + 772614122 q^{41} - 545038272 q^{42} + 3749722062 q^{43} - 50755584 q^{44} - 1321716548 q^{45} - 1394938624 q^{46} + 1924889212 q^{47} + 58720256 q^{48} + 822161735 q^{49} - 805012448 q^{50} + 5262939047 q^{51} - 3168823296 q^{52} + 1531782992 q^{53} + 295824512 q^{54} + 3851857218 q^{55} + 912654336 q^{56} - 17257259731 q^{57} + 17790744128 q^{58} - 16014164779 q^{59} - 3503935488 q^{60} + 7822116636 q^{61} + 6939975808 q^{62} - 79975953122 q^{63} - 5368709120 q^{64} + 73754374272 q^{65} - 3094015232 q^{66} - 22092583538 q^{67} + 1701132288 q^{68} + 43044165458 q^{69} - 5227997760 q^{70} + 23107180542 q^{71} + 6763675648 q^{72} + 55731754682 q^{73} - 5152020032 q^{74} - 37848703409 q^{75} - 7477467136 q^{76} - 52140560296 q^{77} - 110695592320 q^{78} + 43369591752 q^{79} + 6194987008 q^{80} - 19607689666 q^{81} + 6103740704 q^{82} + 105219370951 q^{83} + 55441248256 q^{84} - 14375063614 q^{85} - 53785859936 q^{86} - 216242949124 q^{87} + 14186872832 q^{88} - 227930374154 q^{89} + 138289668864 q^{90} + 236440118278 q^{91} + 109996521472 q^{92} + 215529449050 q^{93} + 24423998144 q^{94} + 242007717988 q^{95} + 1879048192 q^{96} - 200605898215 q^{97} + 128896464000 q^{98} - 634415317547 q^{99}+O(q^{100}) \) 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9 - 354944 * q^10 - 449801 * q^11 + 108544 * q^12 + 3369596 * q^13 - 5349696 * q^14 + 12264628 * q^15 - 5242880 * q^16 + 1661262 * q^17 - 19177088 * q^18 + 49176291 * q^19 - 370688 * q^20 - 74218796 * q^21 - 5153632 * q^22 - 127653292 * q^23 - 3571712 * q^24 + 33758041 * q^25 - 99025728 * q^26 - 135657199 * q^27 + 156930048 * q^28 + 555960754 * q^29 + 392468096 * q^30 - 13977916 * q^31 + 671088640 * q^32 - 1768265081 * q^33 - 357119936 * q^34 + 584997860 * q^35 - 613666816 * q^36 - 161000626 * q^37 - 1456805888 * q^38 + 1145816470 * q^39 + 193593344 * q^40 + 772614122 * q^41 - 545038272 * q^42 + 3749722062 * q^43 - 50755584 * q^44 - 1321716548 * q^45 - 1394938624 * q^46 + 1924889212 * q^47 + 58720256 * q^48 + 822161735 * q^49 - 805012448 * q^50 + 5262939047 * q^51 - 3168823296 * q^52 + 1531782992 * q^53 + 295824512 * q^54 + 3851857218 * q^55 + 912654336 * q^56 - 17257259731 * q^57 + 17790744128 * q^58 - 16014164779 * q^59 - 3503935488 * q^60 + 7822116636 * q^61 + 6939975808 * q^62 - 79975953122 * q^63 - 5368709120 * q^64 + 73754374272 * q^65 - 3094015232 * q^66 - 22092583538 * q^67 + 1701132288 * q^68 + 43044165458 * q^69 - 5227997760 * q^70 + 23107180542 * q^71 + 6763675648 * q^72 + 55731754682 * q^73 - 5152020032 * q^74 - 37848703409 * q^75 - 7477467136 * q^76 - 52140560296 * q^77 - 110695592320 * q^78 + 43369591752 * q^79 + 6194987008 * q^80 - 19607689666 * q^81 + 6103740704 * q^82 + 105219370951 * q^83 + 55441248256 * q^84 - 14375063614 * q^85 - 53785859936 * q^86 - 216242949124 * q^87 + 14186872832 * q^88 - 227930374154 * q^89 + 138289668864 * q^90 + 236440118278 * q^91 + 109996521472 * q^92 + 215529449050 * q^93 + 24423998144 * q^94 + 242007717988 * q^95 + 1879048192 * q^96 - 200605898215 * q^97 + 128896464000 * q^98 - 634415317547 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−25.8885	−	18.8091i	−0.572061	−	0.415627i
$2$	−25.8885	−	18.8091i	−0.572061	−	0.415627i
$3$	201.415	−	619.892i	0.478547	−	1.47282i	−0.362566	−	0.931958i	$-0.618099\pi$
$3$	201.415	−	619.892i	0.478547	−	1.47282i	0.841113	−	0.540859i	$-0.181901\pi$
$4$	316.433	+	973.882i	0.154508	+	0.475528i
$5$	932.620	−	677.588i	0.133466	−	0.0969686i	−0.519049	−	0.854744i	$-0.673714\pi$
$5$	932.620	−	677.588i	0.133466	−	0.0969686i	0.652515	+	0.757776i	$0.273714\pi$
$6$	−16874.0	+	12259.7i	−0.885901	+	0.643645i
$7$	−16358.4	−	50346.1i	−0.367877	−	1.13221i	−0.948160	−	0.317794i	$-0.897058\pi$
$7$	−16358.4	−	50346.1i	−0.367877	−	1.13221i	0.580283	−	0.814415i	$-0.302942\pi$
$8$	10125.9	−	31164.2i	0.109254	−	0.336249i
$9$	−200383.	−	145587.i	−1.13117	−	0.821841i
$10$	−36889.0			−0.116653
$11$	131656.	−	517666.i	0.246479	−	0.969148i
$11$	131656.	−	517666.i	0.246479	−	0.969148i
$12$	667436.			0.774306
$13$	283981.	+	206324.i	0.212129	+	0.154121i	0.688776	−	0.724974i	$-0.258148\pi$
$13$	283981.	+	206324.i	0.212129	+	0.154121i	−0.476647	+	0.879095i	$0.658148\pi$
$14$	−523470.	+	1.61108e6i	−0.260128	+	0.800593i
$15$	−232188.	−	714600.i	−0.0789473	−	0.242975i
$16$	−848316.	+	616338.i	−0.202254	+	0.146946i
$17$	−1.28534e6	+	933855.i	−0.219558	+	0.159518i	−0.692128	−	0.721775i	$-0.743327\pi$
$17$	−1.28534e6	+	933855.i	−0.219558	+	0.159518i	0.472570	+	0.881293i	$0.343327\pi$
$18$	2.44926e6	+	7.53805e6i	0.305518	+	0.940287i
$19$	379520.	−	1.16804e6i	0.0351633	−	0.108222i	−0.931934	−	0.362627i	$-0.881880\pi$
$19$	379520.	−	1.16804e6i	0.0351633	−	0.108222i	0.967098	+	0.254406i	$0.0818798\pi$
$20$	955003.	+	693851.i	0.0667329	+	0.0484843i
$21$	−3.45040e7			−1.84358
$22$	−1.31452e7	+	1.09253e7i	−0.543805	+	0.451969i
$23$	−3.80447e7			−1.23251			−0.616256	−	0.787546i	$-0.711351\pi$
$23$	−3.80447e7			−1.23251			−0.616256	+	0.787546i	$0.711351\pi$
$24$	−1.72789e7	−	1.25539e7i	−0.442951	−	0.321822i
$25$	−1.46781e7	+	4.51744e7i	−0.300607	+	0.925173i
$26$	−3.47107e6	−	1.06829e7i	−0.0572941	−	0.176333i
$27$	−3.71964e7	+	2.70248e7i	−0.498885	+	0.362461i
$28$	4.38548e7	−	3.18624e7i	0.481557	−	0.349872i
$29$	4.89155e7	+	1.50546e8i	0.442851	+	1.36295i	0.884824	+	0.465926i	$0.154279\pi$
$29$	4.89155e7	+	1.50546e8i	0.442851	+	1.36295i	−0.441973	+	0.897028i	$0.645721\pi$
$30$	−7.43001e6	+	2.28672e7i	−0.0558242	+	0.171809i
$31$	1.37249e8	+	9.97173e7i	0.861034	+	0.625578i	0.928166	−	0.372166i	$-0.121385\pi$
$31$	1.37249e8	+	9.97173e7i	0.861034	+	0.625578i	−0.0671321	+	0.997744i	$0.521385\pi$
$32$	3.35544e7			0.176777
$33$	−2.94380e8	−	1.85878e8i	−1.30943	−	0.826802i
$34$	5.08406e7			0.191901
$35$	−4.93701e7	−	3.58695e7i	−0.158888	−	0.115439i
$36$	7.83764e7	−	2.41218e8i	0.216034	−	0.664883i
$37$	−1.92238e8	−	5.91649e8i	−0.455754	−	1.40267i	−0.870248	−	0.492614i	$-0.836041\pi$
$37$	−1.92238e8	−	5.91649e8i	−0.455754	−	1.40267i	0.414494	−	0.910052i	$-0.363959\pi$
$38$	−3.17951e7	+	2.31005e7i	−0.0650953	+	0.0472945i
$39$	1.85096e8	−	1.34480e8i	0.328506	−	0.238673i
$40$	−1.16729e7	−	3.59256e7i	−0.0180239	−	0.0554720i
$41$	−1.13695e8	+	3.49917e8i	−0.153260	+	0.471686i	−0.997980	−	0.0635217i	$-0.979767\pi$
$41$	−1.13695e8	+	3.49917e8i	−0.153260	+	0.471686i	0.844720	+	0.535208i	$0.179767\pi$
$42$	8.93257e8	+	6.48989e8i	1.05464	+	0.766243i
$43$	−5.05494e6			−0.00524372			−0.00262186	−	0.999997i	$-0.500835\pi$
$43$	−5.05494e6			−0.00524372			−0.00262186	+	0.999997i	$0.500835\pi$
$44$	5.45806e8	−	3.55896e7i	0.498940	−	0.0325337i
$45$	−2.85529e8			−0.230665
$46$	9.84923e8	+	7.15588e8i	0.705073	+	0.512265i
$47$	6.56469e8	−	2.02040e9i	0.417519	−	1.28499i	−0.492460	−	0.870335i	$-0.663902\pi$
$47$	6.56469e8	−	2.02040e9i	0.417519	−	1.28499i	0.909979	−	0.414655i	$-0.136098\pi$
$48$	2.11199e8	+	6.50004e8i	0.119637	+	0.368204i
$49$	−6.67440e8	+	4.84923e8i	−0.337547	+	0.245242i
$50$	1.22969e9	−	8.93419e8i	0.556492	−	0.404315i
$51$	3.20002e8	+	9.84865e8i	0.129872	+	0.399706i
$52$	−1.11074e8	+	3.41851e8i	−0.0405130	+	0.124686i
$53$	4.41119e8	+	3.20492e8i	0.144890	+	0.105269i	0.657869	−	0.753132i	$-0.271458\pi$
$53$	4.41119e8	+	3.20492e8i	0.144890	+	0.105269i	−0.512979	+	0.858401i	$0.671458\pi$
$54$	1.47127e9			0.436041
$55$	−2.27980e8	−	5.71995e8i	−0.0610803	−	0.153249i
$56$	−1.73464e9			−0.420896
$57$	−6.47618e8	−	4.70522e8i	−0.142563	−	0.103578i
$58$	1.56530e9	−	4.81749e9i	0.313143	−	0.963755i
$59$	−2.93263e9	−	9.02572e9i	−0.534038	−	1.64360i	−0.745719	−	0.666260i	$-0.767894\pi$
$59$	−2.93263e9	−	9.02572e9i	−0.534038	−	1.64360i	0.211682	−	0.977339i	$-0.432106\pi$
$60$	6.22464e8	−	4.52247e8i	0.103343	−	0.0750833i
$61$	−1.00967e10	+	7.33571e9i	−1.53062	+	1.11206i	−0.574727	+	0.818345i	$0.694892\pi$
$61$	−1.00967e10	+	7.33571e9i	−1.53062	+	1.11206i	−0.955893	+	0.293715i	$0.905108\pi$
$62$	−1.67758e9	−	5.16307e9i	−0.232557	−	0.715738i
$63$	−4.05177e9	+	1.24701e10i	−0.514365	+	1.58305i
$64$	−8.68675e8	−	6.31130e8i	−0.101127	−	0.0734732i
$65$	4.04649e8			0.0432568
$66$	4.12485e9	+	1.03491e10i	0.405431	+	1.01721i
$67$	−8.21768e8			−0.0743597			−0.0371799	−	0.999309i	$-0.511837\pi$
$67$	−8.21768e8			−0.0743597			−0.0371799	+	0.999309i	$0.511837\pi$
$68$	−1.31619e9	−	9.56268e8i	−0.109779	−	0.0797592i
$69$	−7.66278e9	+	2.35836e10i	−0.589816	+	1.81527i
$70$	6.03447e8	+	1.85722e9i	0.0429141	+	0.132076i
$71$	2.10989e10	−	1.53292e10i	1.38784	−	1.00832i	0.391738	−	0.920077i	$-0.371874\pi$
$71$	2.10989e10	−	1.53292e10i	1.38784	−	1.00832i	0.996099	−	0.0882452i	$-0.0281259\pi$
$72$	−6.56614e9	+	4.77058e9i	−0.399928	+	0.290565i
$73$	−7.55965e9	−	2.32662e10i	−0.426801	−	1.31356i	−0.901259	−	0.433281i	$-0.857356\pi$
$73$	−7.55965e9	−	2.32662e10i	−0.426801	−	1.31356i	0.474458	−	0.880278i	$-0.342644\pi$
$74$	−6.15163e9	+	1.89328e10i	−0.322267	+	0.991835i
$75$	2.50469e10	+	1.81976e10i	1.21876	+	0.885478i
$76$	1.25763e9			0.0568954
$77$	−2.82162e10	+	1.83985e9i	−1.18795	+	0.0774612i
$78$	−7.32134e9			−0.287124
$79$	−2.01302e10	−	1.46254e10i	−0.736035	−	0.534761i	0.155432	−	0.987847i	$-0.450323\pi$
$79$	−2.01302e10	−	1.46254e10i	−0.736035	−	0.534761i	−0.891467	+	0.453086i	$0.850323\pi$
$80$	−3.73534e8	+	1.14962e9i	−0.0127448	+	0.0392246i
$81$	−4.29821e9	−	1.32285e10i	−0.136968	−	0.421545i
$82$	9.52502e9	−	6.92033e9i	0.283720	−	0.206135i
$83$	2.15075e10	−	1.56261e10i	0.599322	−	0.435433i	−0.246316	−	0.969189i	$-0.579220\pi$
$83$	2.15075e10	−	1.56261e10i	0.599322	−	0.435433i	0.845638	+	0.533757i	$0.179220\pi$
$84$	−1.09182e10	−	3.36028e10i	−0.284849	−	0.876676i
$85$	−5.65966e8	+	1.74187e9i	−0.0138352	+	0.0425805i
$86$	1.30865e8	+	9.50789e7i	0.00299973	+	0.00217943i
$87$	1.03175e11			2.21931
$88$	−1.47995e10	−	9.34477e9i	−0.298946	−	0.188762i
$89$	1.88613e10			0.358036			0.179018	−	0.983846i	$-0.442708\pi$
$89$	1.88613e10			0.358036			0.179018	+	0.983846i	$0.442708\pi$
$90$	7.39193e9	+	5.37055e9i	0.131954	+	0.0958705i
$91$	5.74213e9	−	1.76725e10i	0.0964595	−	0.296872i
$92$	−1.20386e10	−	3.70511e10i	−0.190434	−	0.586095i
$93$	8.94580e10	−	6.49950e10i	1.33341	−	0.968777i
$94$	−5.49970e10	+	3.99577e10i	−0.772923	+	0.561561i
$95$	−4.37504e8	−	1.34650e9i	−0.00580099	−	0.0178536i
$96$	6.75837e9	−	2.08001e10i	0.0845960	−	0.260360i
$97$	9.34412e10	+	6.78890e10i	1.10483	+	0.802703i	0.981841	−	0.189706i	$-0.0607534\pi$
$97$	9.34412e10	+	6.78890e10i	1.10483	+	0.802703i	0.122985	+	0.992409i	$0.460753\pi$
$98$	2.64000e10			0.295027
$99$	−1.01747e11	+	8.45641e10i	−1.07529	+	0.893701i
$100$	−4.86392e10			−0.486392
$101$	8.22152e10	+	5.97328e10i	0.778367	+	0.565517i	0.904489	−	0.426498i	$-0.140253\pi$
$101$	8.22152e10	+	5.97328e10i	0.778367	+	0.565517i	−0.126121	+	0.992015i	$0.540253\pi$
$102$	1.02401e10	−	3.15157e10i	0.0918337	−	0.282635i
$103$	−1.14165e10	−	3.51364e10i	−0.0970350	−	0.298643i	0.890744	−	0.454506i	$-0.150184\pi$
$103$	−1.14165e10	−	3.51364e10i	−0.0970350	−	0.298643i	−0.987779	+	0.155863i	$0.950184\pi$
$104$	9.30548e9	−	6.76082e9i	0.0749990	−	0.0544899i
$105$	−3.21791e10	+	2.33795e10i	−0.246055	+	0.178770i
$106$	−5.39176e9	−	1.65941e10i	−0.0391335	−	0.120440i
$107$	−5.60731e10	+	1.72575e11i	−0.386495	+	1.18951i	0.548896	+	0.835891i	$0.315048\pi$
$107$	−5.60731e10	+	1.72575e11i	−0.386495	+	1.18951i	−0.935390	+	0.353617i	$0.884952\pi$
$108$	−3.80891e10	−	2.76734e10i	−0.249442	−	0.181231i
$109$	−9.82702e10			−0.611753			−0.305876	−	0.952071i	$-0.598949\pi$
$109$	−9.82702e10			−0.611753			−0.305876	+	0.952071i	$0.598949\pi$
$110$	−4.85666e9	+	1.90962e10i	−0.0287526	+	0.113054i
$111$	−4.05478e11			−2.28397
$112$	4.49073e10	+	3.26271e10i	0.240779	+	0.174936i
$113$	1.19921e11	−	3.69080e11i	0.612302	−	1.88447i	0.176918	−	0.984226i	$-0.443387\pi$
$113$	1.19921e11	−	3.69080e11i	0.612302	−	1.88447i	0.435383	−	0.900245i	$-0.356613\pi$
$114$	7.91578e9	+	2.43623e10i	0.0385050	+	0.118506i
$115$	−3.54813e10	+	2.57787e10i	−0.164498	+	0.119515i
$116$	−1.31136e11	+	9.52758e10i	−0.579699	+	0.421176i
$117$	−2.68668e10	−	8.26875e10i	−0.113291	−	0.348673i
$118$	−9.38443e10	+	2.88823e11i	−0.377622	+	1.16220i
$119$	6.80422e10	+	4.94355e10i	0.261378	+	0.189903i
$120$	−2.46211e10			−0.0903254
$121$	−2.50645e11	−	1.36308e11i	−0.878496	−	0.477750i
$122$	3.99368e11			1.33781
$123$	1.94011e11	+	1.40957e11i	0.621366	+	0.451449i
$124$	−5.36827e10	+	1.65218e11i	−0.164443	+	0.506103i
$125$	3.43146e10	+	1.05610e11i	0.100571	+	0.309527i
$126$	3.39445e11	−	2.46621e11i	0.952208	−	0.691820i
$127$	−8.90626e10	+	6.47078e10i	−0.239208	+	0.173794i	−0.700930	−	0.713230i	$-0.747232\pi$
$127$	−8.90626e10	+	6.47078e10i	−0.239208	+	0.173794i	0.461723	+	0.887024i	$0.347232\pi$
$128$	1.06177e10	+	3.26781e10i	0.0273135	+	0.0840623i
$129$	−1.01814e9	+	3.13351e9i	−0.00250937	+	0.00772304i
$130$	−1.04758e10	−	7.61109e9i	−0.0247456	−	0.0179787i
$131$	−1.31320e11			−0.297398			−0.148699	−	0.988883i	$-0.547509\pi$
$131$	−1.31320e11			−0.297398			−0.148699	+	0.988883i	$0.547509\pi$
$132$	8.78718e10	−	3.45509e11i	0.190850	−	0.750417i
$133$	−6.50147e10			−0.135465
$134$	2.12744e10	+	1.54567e10i	0.0425383	+	0.0309059i
$135$	−1.63785e10	+	5.04077e10i	−0.0314367	+	0.0967523i
$136$	1.60877e10	+	4.95128e10i	0.0296503	+	0.0912543i
$137$	1.02139e11	−	7.42081e10i	0.180812	−	0.131368i	−0.493698	−	0.869634i	$-0.664355\pi$
$137$	1.02139e11	−	7.42081e10i	0.180812	−	0.131368i	0.674510	+	0.738266i	$0.264355\pi$
$138$	6.41965e11	−	4.66415e11i	1.09188	−	0.793300i
$139$	2.20843e11	+	6.79685e11i	0.360996	+	1.11103i	0.952451	+	0.304693i	$0.0985538\pi$
$139$	2.20843e11	+	6.79685e11i	0.360996	+	1.11103i	−0.591455	+	0.806338i	$0.701446\pi$
$140$	1.93103e10	−	5.94310e10i	0.0303448	−	0.0933918i
$141$	−1.12021e12	−	8.13879e11i	−1.69275	−	1.22986i
$142$	−8.34548e11			−1.21301
$143$	1.44195e11	−	1.19843e11i	0.201651	−	0.167597i
$144$	2.59718e11			0.349550
$145$	1.47628e11	+	1.07258e11i	0.191269	+	0.138965i
$146$	−2.41909e11	+	7.44518e11i	−0.301794	+	0.928827i
$147$	1.66168e11	+	5.11411e11i	0.199665	+	0.614504i
$148$	5.15365e11	−	3.74435e11i	0.596590	−	0.433448i
$149$	1.27879e12	−	9.29099e11i	1.42652	−	1.03642i	0.435863	−	0.900013i	$-0.356443\pi$
$149$	1.27879e12	−	9.29099e11i	1.42652	−	1.03642i	0.990652	−	0.136411i	$-0.0435568\pi$
$150$	−3.06146e11	−	9.42220e11i	−0.329175	−	1.01310i
$151$	1.82995e10	−	5.63199e10i	0.0189699	−	0.0583834i	−0.941123	−	0.338063i	$-0.890228\pi$
$151$	1.82995e10	−	5.63199e10i	0.0189699	−	0.0583834i	0.960093	+	0.279680i	$0.0902283\pi$
$152$	−3.25581e10	−	2.36549e10i	−0.0325477	−	0.0236473i
$153$	3.93517e11			0.379456
$154$	7.65081e11	+	4.83090e11i	0.711777	+	0.449432i
$155$	1.95569e11			0.175580
$156$	1.89539e11	+	1.37708e11i	0.164253	+	0.119337i
$157$	−4.57632e10	+	1.40845e11i	−0.0382885	+	0.117840i	−0.968374	−	0.249504i	$-0.919733\pi$
$157$	−4.57632e10	+	1.40845e11i	−0.0382885	+	0.117840i	0.930085	+	0.367343i	$0.119733\pi$
$158$	2.46049e11	+	7.57262e11i	0.198796	+	0.611832i
$159$	2.87518e11	−	2.08894e11i	0.224379	−	0.163021i
$160$	3.12935e10	−	2.27361e10i	0.0235936	−	0.0171418i
$161$	6.22352e11	+	1.91540e12i	0.453413	+	1.39546i
$162$	−1.37543e11	+	4.23313e11i	−0.0968512	+	0.298077i
$163$	−1.84734e12	−	1.34217e12i	−1.25752	−	0.913644i	−0.258890	−	0.965907i	$-0.583357\pi$
$163$	−1.84734e12	−	1.34217e12i	−1.25752	−	0.913644i	−0.998633	+	0.0522629i	$0.983357\pi$
$164$	−3.76754e11			−0.247980
$165$	−4.00493e11	+	2.61144e10i	−0.254937	+	0.0166234i
$166$	−8.50711e11			−0.523826
$167$	1.06815e12	+	7.76059e11i	0.636346	+	0.462332i	0.858593	−	0.512658i	$-0.171339\pi$
$167$	1.06815e12	+	7.76059e11i	0.636346	+	0.462332i	−0.222247	+	0.974990i	$0.571339\pi$
$168$	−3.49383e11	+	1.07529e12i	−0.201419	+	0.619904i
$169$	−5.15733e11	−	1.58726e12i	−0.287771	−	0.885670i
$170$	4.74150e10	−	3.44490e10i	0.0256122	−	0.0186084i
$171$	−2.46101e11	+	1.78802e11i	−0.128716	+	0.0935179i
$172$	−1.59955e9	−	4.92291e9i	−0.000810199	−	0.00249353i
$173$	9.91377e11	−	3.05114e12i	0.486391	−	1.49696i	−0.343566	−	0.939129i	$-0.611635\pi$
$173$	9.91377e11	−	3.05114e12i	0.486391	−	1.49696i	0.829957	−	0.557828i	$-0.188365\pi$
$174$	−2.67105e12	−	1.94063e12i	−1.26958	−	0.922404i
$175$	2.51447e12			1.15807
$176$	2.07371e11	+	5.20289e11i	0.0925612	+	0.232234i
$177$	−6.18565e12			−2.67628
$178$	−4.88291e11	−	3.54764e11i	−0.204818	−	0.148809i
$179$	4.73031e11	−	1.45584e12i	0.192397	−	0.592137i	−0.807600	−	0.589730i	$-0.799234\pi$
$179$	4.73031e11	−	1.45584e12i	0.192397	−	0.592137i	0.999997	−	0.00240655i	$-0.000766031\pi$
$180$	−9.03509e10	−	2.78071e11i	−0.0356397	−	0.109688i
$181$	−2.48961e12	+	1.80881e12i	−0.952576	+	0.692087i	−0.951415	−	0.307912i	$-0.900370\pi$
$181$	−2.48961e12	+	1.80881e12i	−0.952576	+	0.692087i	−0.00116121	+	0.999999i	$0.500370\pi$
$182$	−4.81059e11	+	3.49510e11i	−0.178569	+	0.129738i
$183$	2.51371e12	+	7.73641e12i	0.905388	+	2.78650i
$184$	−3.85236e11	+	1.18563e12i	−0.134657	+	0.414431i
$185$	−5.80180e11	−	4.21525e11i	−0.196842	−	0.143014i
$186$	−3.53844e12			−1.16544
$187$	3.14203e11	+	7.88326e11i	0.100480	+	0.252102i
$188$	2.17536e12			0.675559
$189$	1.96907e12	+	1.43061e12i	0.593910	+	0.431501i
$190$	−1.40001e10	+	4.30879e10i	−0.00410192	+	0.0126244i
$191$	1.20649e12	+	3.71320e12i	0.343432	+	1.05697i	0.962418	+	0.271572i	$0.0875436\pi$
$191$	1.20649e12	+	3.71320e12i	0.343432	+	1.05697i	−0.618986	+	0.785402i	$0.712456\pi$
$192$	−5.66196e11	+	4.11366e11i	−0.156607	+	0.113781i
$193$	3.60168e12	−	2.61678e12i	0.968145	−	0.703399i	0.0131170	−	0.999914i	$-0.495825\pi$
$193$	3.60168e12	−	2.61678e12i	0.968145	−	0.703399i	0.955028	+	0.296515i	$0.0958246\pi$
$194$	−1.14212e12	−	3.51509e12i	−0.298403	−	0.918391i
$195$	8.15024e10	−	2.50838e11i	0.0207005	−	0.0637094i
$196$	−6.83458e11	−	4.96562e11i	−0.168773	−	0.122621i
$197$	−8.65531e11			−0.207835			−0.103917	−	0.994586i	$-0.533138\pi$
$197$	−8.65531e11			−0.207835			−0.103917	+	0.994586i	$0.533138\pi$
$198$	4.22465e12	−	2.75471e11i	0.986581	−	0.0643306i
$199$	−1.10678e11			−0.0251402			−0.0125701	−	0.999921i	$-0.504001\pi$
$199$	−1.10678e11			−0.0251402			−0.0125701	+	0.999921i	$0.504001\pi$
$200$	1.25920e12	+	9.14861e11i	0.278246	+	0.202158i
$201$	−1.65516e11	+	5.09407e11i	−0.0355847	+	0.109518i
$202$	−1.00491e12	−	3.09279e12i	−0.210230	−	0.647021i
$203$	6.77924e12	−	4.92541e12i	1.38023	−	1.00280i
$204$	−8.57883e11	+	6.23289e11i	−0.170005	+	0.123516i
$205$	1.31065e11	+	4.03378e11i	0.0252838	+	0.0778154i
$206$	−3.65328e11	+	1.12436e12i	−0.0686141	+	0.211172i
$207$	7.62351e12	+	5.53880e12i	1.39418	+	1.01293i
$208$	−3.68070e11			−0.0655515
$209$	−5.54690e11	−	3.50244e11i	−0.0962156	−	0.0607528i
$210$	1.27282e12			0.215060
$211$	−7.45458e12	−	5.41607e12i	−1.22707	−	0.891519i	−0.230404	−	0.973095i	$-0.574005\pi$
$211$	−7.45458e12	−	5.41607e12i	−1.22707	−	0.891519i	−0.996667	+	0.0815760i	$0.974005\pi$
$212$	−1.72536e11	+	5.31013e11i	−0.0276716	+	0.0851643i
$213$	−5.25283e12	−	1.61666e13i	−0.820929	−	2.52656i
$214$	4.69764e12	−	3.41303e12i	0.715490	−	0.519834i
$215$	−4.71434e9	+	3.42517e9i	−0.000699857	+	0.000508476i
$216$	4.65560e11	+	1.43285e12i	0.0673721	+	0.207350i
$217$	2.77520e12	−	8.54118e12i	0.391530	−	1.20501i
$218$	2.54407e12	+	1.84838e12i	0.349960	+	0.254261i
$219$	−1.59452e13			−2.13888
$220$	4.84915e11	−	4.03024e11i	0.0634367	−	0.0527237i
$221$	−5.57689e11			−0.0711598
$222$	1.04972e13	+	7.62668e12i	1.30657	+	0.949280i
$223$	5.58945e11	−	1.72026e12i	0.0678723	−	0.208889i	−0.911368	−	0.411593i	$-0.864973\pi$
$223$	5.58945e11	−	1.72026e12i	0.0678723	−	0.208889i	0.979240	+	0.202703i	$0.0649727\pi$
$224$	−5.48898e11	−	1.68933e12i	−0.0650321	−	0.200148i
$225$	9.51803e12	−	6.91525e12i	1.10038	−	0.799474i
$226$	−1.00467e13	+	7.29933e12i	−1.13351	+	0.823544i
$227$	2.06516e12	+	6.35589e12i	0.227410	+	0.699898i	0.998038	+	0.0626117i	$0.0199430\pi$
$227$	2.06516e12	+	6.35589e12i	0.227410	+	0.699898i	−0.770627	+	0.637286i	$0.780057\pi$
$228$	2.53305e11	−	7.79593e11i	0.0272272	−	0.0837966i
$229$	7.44830e12	+	5.41151e12i	0.781560	+	0.567836i	0.905447	−	0.424460i	$-0.139536\pi$
$229$	7.44830e12	+	5.41151e12i	0.781560	+	0.567836i	−0.123887	+	0.992296i	$0.539536\pi$
$230$	1.40343e12			0.143777
$231$	−4.54265e12	+	1.78615e13i	−0.454405	+	1.78671i
$232$	5.18697e12			0.506676
$233$	6.86372e12	+	4.98679e12i	0.654790	+	0.475733i	0.864900	−	0.501945i	$-0.167382\pi$
$233$	6.86372e12	+	4.98679e12i	0.654790	+	0.475733i	−0.210109	+	0.977678i	$0.567382\pi$
$234$	−8.59738e11	+	2.64600e12i	−0.0801086	+	0.246549i
$235$	−7.56765e11	−	2.32908e12i	−0.0688792	−	0.211988i
$236$	7.86200e12	−	5.71208e12i	0.699064	−	0.507900i
$237$	−1.31207e13	+	9.53275e12i	−1.13983	+	0.828137i
$238$	−8.31673e11	−	2.55963e12i	−0.0705959	−	0.217272i
$239$	−3.26692e12	+	1.00545e13i	−0.270988	+	0.834014i	0.719265	+	0.694735i	$0.244479\pi$
$239$	−3.26692e12	+	1.00545e13i	−0.270988	+	0.834014i	−0.990253	+	0.139279i	$0.955521\pi$
$240$	6.37403e11	+	4.63101e11i	0.0516717	+	0.0375417i
$241$	−1.04110e13			−0.824898			−0.412449	−	0.910981i	$-0.635326\pi$
$241$	−1.04110e13			−0.824898			−0.412449	+	0.910981i	$0.635326\pi$
$242$	3.92501e12	+	8.24322e12i	0.303988	+	0.638429i
$243$	−1.72107e13			−1.30306
$244$	−1.03391e13	−	7.51177e12i	−0.765310	−	0.556030i
$245$	−2.93890e11	+	9.04499e11i	−0.0212702	+	0.0654628i
$246$	−2.37137e12	−	7.29834e12i	−0.167825	−	0.516513i
$247$	3.48771e11	−	2.53397e11i	0.0241383	−	0.0175375i
$248$	4.49738e12	−	3.26754e12i	0.304421	−	0.221175i
$249$	−5.35456e12	−	1.64796e13i	−0.354509	−	1.09107i
$250$	1.09807e12	−	3.37951e12i	0.0711147	−	0.218868i
$251$	−2.86381e12	−	2.08068e12i	−0.181442	−	0.131826i	0.493357	−	0.869827i	$-0.335770\pi$
$251$	−2.86381e12	−	2.08068e12i	−0.181442	−	0.131826i	−0.674799	+	0.738001i	$0.735770\pi$
$252$	−1.34265e13			−0.832260
$253$	−5.00881e12	+	1.96945e13i	−0.303789	+	1.19449i
$254$	3.52280e12			0.209075
$255$	9.65774e11	+	7.01676e11i	0.0560925	+	0.0407536i
$256$	3.39768e11	−	1.04570e12i	0.0193136	−	0.0594410i
$257$	−1.68096e12	−	5.17347e12i	−0.0935245	−	0.287839i	0.893342	−	0.449378i	$-0.148354\pi$
$257$	−1.68096e12	−	5.17347e12i	−0.0935245	−	0.287839i	−0.986866	+	0.161539i	$0.948354\pi$
$258$	8.52968e10	−	6.19718e10i	0.00464541	−	0.00337509i
$259$	−2.66425e13	+	1.93569e13i	−1.42045	+	1.03202i
$260$	1.28044e11	+	3.94080e11i	0.00668355	+	0.0205699i
$261$	1.21157e13	−	3.72884e13i	0.619194	−	1.90568i
$262$	3.39968e12	+	2.47001e12i	0.170130	+	0.123607i
$263$	2.74640e13			1.34588			0.672941	−	0.739696i	$-0.265031\pi$
$263$	2.74640e13			1.34588			0.672941	+	0.739696i	$0.265031\pi$
$264$	−8.77360e12	+	7.29193e12i	−0.421072	+	0.349962i
$265$	6.28559e11			0.0295456
$266$	1.68314e12	+	1.22287e12i	0.0774944	+	0.0563030i
$267$	3.79895e12	−	1.16920e13i	0.171337	−	0.527321i
$268$	−2.60035e11	−	8.00305e11i	−0.0114892	−	0.0353602i
$269$	2.11620e13	−	1.53751e13i	0.916050	−	0.665549i	−0.0264877	−	0.999649i	$-0.508432\pi$
$269$	2.11620e13	−	1.53751e13i	0.916050	−	0.665549i	0.942538	+	0.334100i	$0.108432\pi$
$270$	1.37214e12	−	9.96918e11i	0.0581966	−	0.0422823i
$271$	1.15868e13	+	3.56606e13i	0.481542	+	1.48203i	0.836928	+	0.547313i	$0.184349\pi$
$271$	1.15868e13	+	3.56606e13i	0.481542	+	1.48203i	−0.355386	+	0.934720i	$0.615651\pi$
$272$	5.14806e11	−	1.58441e12i	0.0209659	−	0.0645265i
$273$	−9.79846e12	−	7.11899e12i	−0.391078	−	0.284135i
$274$	−4.04001e12			−0.158035
$275$	2.14528e13	+	1.35458e13i	0.822536	+	0.519368i
$276$	−2.53924e13			−0.954342
$277$	1.89172e13	+	1.37442e13i	0.696977	+	0.506383i	0.878946	−	0.476921i	$-0.158247\pi$
$277$	1.89172e13	+	1.37442e13i	0.696977	+	0.506383i	−0.181969	+	0.983304i	$0.558247\pi$
$278$	7.06698e12	−	2.17499e13i	0.255263	−	0.785618i
$279$	−1.29849e13	−	3.99633e13i	−0.459848	−	1.41527i
$280$	−1.61776e12	+	1.17537e12i	−0.0561753	+	0.0408137i
$281$	−4.98335e12	+	3.62062e12i	−0.169682	+	0.123282i	−0.669385	−	0.742915i	$-0.733442\pi$
$281$	−4.98335e12	+	3.62062e12i	−0.169682	+	0.123282i	0.499703	+	0.866197i	$0.333442\pi$
$282$	1.36922e13	+	4.21403e13i	0.457197	+	1.40711i
$283$	8.21002e12	−	2.52678e13i	0.268855	−	0.827452i	−0.721925	−	0.691972i	$-0.756742\pi$
$283$	8.21002e12	−	2.52678e13i	0.268855	−	0.827452i	0.990780	−	0.135480i	$-0.0432577\pi$
$284$	2.16052e13	+	1.56971e13i	0.693918	+	0.504161i
$285$	−9.22803e11			−0.0290711
$286$	−5.98714e12	+	3.90395e11i	−0.185015	+	0.0120640i
$287$	1.94768e13			0.590428
$288$	−6.72373e12	−	4.88508e12i	−0.199964	−	0.145282i
$289$	−9.81058e12	+	3.01939e13i	−0.286257	+	0.881009i
$290$	−1.80445e12	−	5.55351e12i	−0.0516600	−	0.158993i
$291$	6.09043e13	−	4.42495e13i	1.71095	−	1.24308i
$292$	2.02664e13	−	1.47244e13i	0.558690	−	0.405912i
$293$	7.06225e12	+	2.17354e13i	0.191061	+	0.588024i	1.00000		0.000132190i	$4.20775e-5\pi$
$293$	7.06225e12	+	2.17354e13i	0.191061	+	0.588024i	−0.808939	+	0.587892i	$0.799958\pi$
$294$	5.31736e12	−	1.63652e13i	0.141184	−	0.434520i
$295$	−8.85076e12	−	6.43045e12i	−0.230653	−	0.167579i
$296$	−2.03848e13			−0.521438
$297$	9.09269e12	+	2.28133e13i	0.228314	+	0.572833i
$298$	−5.05817e13			−1.24682
$299$	−1.08040e13	−	7.84954e12i	−0.261452	−	0.189956i
$300$	−9.79667e12	+	3.01510e13i	−0.232762	+	0.716367i
$301$	8.26909e10	+	2.54496e11i	0.00192904	+	0.00593698i
$302$	−1.53308e12	+	1.11384e12i	−0.0351176	+	0.0255145i
$303$	5.35873e13	−	3.89334e13i	1.20539	−	0.875766i
$304$	3.97955e11	+	1.22478e12i	0.00879083	+	0.0270554i
$305$	−4.44584e12	+	1.36829e13i	−0.0964505	+	0.296844i
$306$	−1.01876e13	−	7.40172e12i	−0.217072	−	0.157712i
$307$	−8.74661e13			−1.83054			−0.915269	−	0.402843i	$-0.868022\pi$
$307$	−8.74661e13			−1.83054			−0.915269	+	0.402843i	$0.868022\pi$
$308$	−1.07203e13	−	2.68970e13i	−0.220384	−	0.552936i
$309$	−2.40802e13			−0.486282
$310$	−5.06299e12	−	3.67848e12i	−0.100443	−	0.0729758i
$311$	−4.92569e12	+	1.51597e13i	−0.0960030	+	0.295467i	−0.987514	−	0.157533i	$-0.949646\pi$
$311$	−4.92569e12	+	1.51597e13i	−0.0960030	+	0.295467i	0.891511	+	0.453000i	$0.149646\pi$
$312$	−2.31672e12	−	7.13012e12i	−0.0443632	−	0.136536i
$313$	−7.54874e12	+	5.48448e12i	−0.142030	+	0.103191i	−0.656531	−	0.754299i	$-0.727977\pi$
$313$	−7.54874e12	+	5.48448e12i	−0.142030	+	0.103191i	0.514501	+	0.857490i	$0.327977\pi$
$314$	3.83391e12	−	2.78550e12i	0.0708808	−	0.0514979i
$315$	4.67081e12	+	1.43753e13i	0.0848563	+	0.261161i
$316$	7.87358e12	−	2.42324e13i	0.140570	−	0.432631i
$317$	−4.90521e13	−	3.56384e13i	−0.860659	−	0.625306i	0.0674049	−	0.997726i	$-0.478528\pi$
$317$	−4.90521e13	−	3.56384e13i	−0.860659	−	0.625306i	−0.928064	+	0.372420i	$0.878528\pi$
$318$	−1.13726e13			−0.196114
$319$	8.43728e13	−	5.50158e12i	1.43006	−	0.0932478i
$320$	−1.23779e12			−0.0206216
$321$	9.56839e13	+	6.95184e13i	1.56697	+	1.13847i
$322$	1.99153e13	−	6.12929e13i	0.320611	−	0.986741i
$323$	6.02970e11	+	1.85575e12i	0.00954293	+	0.0293701i
$324$	1.15229e13	−	8.37190e12i	0.179294	−	0.130265i
$325$	−1.34889e13	+	9.80023e12i	−0.206356	+	0.149926i
$326$	2.25799e13	+	6.94939e13i	0.339645	+	1.04532i
$327$	−1.97931e13	+	6.09169e13i	−0.292753	+	0.901000i
$328$	9.75362e12	+	7.08642e12i	0.141860	+	0.103067i
$329$	−1.12458e14			−1.60847
$330$	1.08594e13	+	6.85687e12i	0.152749	+	0.0964493i
$331$	3.11313e13			0.430669			0.215334	−	0.976540i	$-0.430916\pi$
$331$	3.11313e13			0.430669			0.215334	+	0.976540i	$0.430916\pi$
$332$	2.20237e13	+	1.60011e13i	0.299661	+	0.217716i
$333$	−4.76149e13	+	1.46544e14i	−0.637235	+	1.96121i
$334$	−1.30560e13	−	4.01821e13i	−0.171871	−	0.528965i
$335$	−7.66398e11	+	5.56821e11i	−0.00992448	+	0.00721056i
$336$	2.92703e13	−	2.12661e13i	0.372873	−	0.270908i
$337$	3.43109e12	+	1.05598e13i	0.0429999	+	0.132340i	0.970252	−	0.242098i	$-0.0778356\pi$
$337$	3.43109e12	+	1.05598e13i	0.0429999	+	0.132340i	−0.927252	+	0.374438i	$0.877836\pi$
$338$	−1.65034e13	+	5.07924e13i	−0.203485	+	0.626263i
$339$	−2.04636e14	−	1.48677e14i	−2.48247	−	1.80362i
$340$	−1.87546e12			−0.0223859
$341$	6.96900e13	−	5.79209e13i	0.818505	−	0.680277i
$342$	9.73430e12			0.112502
$343$	−4.93506e13	−	3.58553e13i	−0.561274	−	0.407789i
$344$	−5.11856e10	+	1.57533e11i	−0.000572897	+	0.00176320i
$345$	8.83352e12	+	2.71868e13i	0.0973035	+	0.299470i
$346$	−8.30547e13	+	6.03428e13i	−0.900421	+	0.654194i
$347$	3.99516e13	−	2.90266e13i	0.426307	−	0.309730i	−0.353864	−	0.935297i	$-0.615132\pi$
$347$	3.99516e13	−	2.90266e13i	0.426307	−	0.309730i	0.780170	+	0.625567i	$0.215132\pi$
$348$	3.26479e13	+	1.00480e14i	0.342902	+	1.05534i
$349$	1.30887e13	−	4.02828e13i	0.135318	−	0.416466i	−0.860321	−	0.509752i	$-0.829737\pi$
$349$	1.30887e13	−	4.02828e13i	0.135318	−	0.416466i	0.995639	+	0.0932858i	$0.0297370\pi$
$350$	−6.50959e13	−	4.72949e13i	−0.662490	−	0.481327i
$351$	−1.61389e13			−0.161691
$352$	4.41764e12	−	1.73700e13i	0.0435718	−	0.171323i
$353$	−1.61855e14			−1.57169			−0.785844	−	0.618425i	$-0.787771\pi$
$353$	−1.61855e14			−1.57169			−0.785844	+	0.618425i	$0.787771\pi$
$354$	1.60137e14	+	1.16347e14i	1.53100	+	1.11234i
$355$	9.29033e12	−	2.85927e13i	0.0874531	−	0.269153i
$356$	5.96834e12	+	1.83687e13i	0.0553195	+	0.170256i
$357$	4.43494e13	−	3.22217e13i	0.404774	−	0.294085i
$358$	−3.96292e13	+	2.87923e13i	−0.356171	+	0.258773i
$359$	−5.50236e13	−	1.69345e14i	−0.487001	−	1.49883i	−0.829062	−	0.559157i	$-0.811125\pi$
$359$	−5.50236e13	−	1.69345e14i	−0.487001	−	1.49883i	0.342061	−	0.939678i	$-0.388875\pi$
$360$	−2.89123e12	+	8.89829e12i	−0.0252010	+	0.0775609i
$361$	9.30223e13	+	6.75847e13i	0.798542	+	0.580174i
$362$	9.84746e13			0.832582
$363$	−1.34980e14	+	1.27918e14i	−1.12404	+	1.06524i
$364$	1.90279e13			0.156075
$365$	−2.28152e13	−	1.65762e13i	−0.184337	−	0.133929i
$366$	8.04388e13	−	2.47565e14i	0.640206	−	1.97035i
$367$	3.95499e13	+	1.21722e14i	0.310086	+	0.954346i	0.977730	+	0.209866i	$0.0673027\pi$
$367$	3.95499e13	+	1.21722e14i	0.310086	+	0.954346i	−0.667644	+	0.744480i	$0.732697\pi$
$368$	3.22739e13	−	2.34484e13i	0.249281	−	0.181113i
$369$	7.37257e13	−	5.35648e13i	0.561014	−	0.407601i
$370$	7.09148e12	+	2.18253e13i	0.0531652	+	0.163626i
$371$	8.91950e12	−	2.74514e13i	0.0658846	−	0.202772i
$372$	9.16050e13	+	6.65549e13i	0.666704	+	0.484389i
$373$	2.14482e14			1.53813			0.769064	−	0.639172i	$-0.220723\pi$
$373$	2.14482e14			1.53813			0.769064	+	0.639172i	$0.220723\pi$
$374$	6.69347e12	−	2.63185e13i	0.0472996	−	0.185980i
$375$	7.23780e13			0.504004
$376$	−5.63170e13	−	4.09167e13i	−0.386461	−	0.280781i
$377$	−1.71703e13	+	5.28447e13i	−0.116118	+	0.357375i
$378$	−2.40677e13	−	7.40729e13i	−0.160410	−	0.493690i
$379$	2.11813e14	−	1.53891e14i	1.39135	−	1.01088i	0.395638	−	0.918407i	$-0.370524\pi$
$379$	2.11813e14	−	1.53891e14i	1.39135	−	1.01088i	0.995715	−	0.0924705i	$-0.0294764\pi$
$380$	1.17289e12	−	8.52154e11i	0.00759359	−	0.00551707i
$381$	2.21733e13	+	6.82423e13i	0.141495	+	0.435478i
$382$	3.86077e13	−	1.18822e14i	0.242843	−	0.747394i
$383$	−9.85926e13	−	7.16317e13i	−0.611295	−	0.444132i	0.238575	−	0.971124i	$-0.423320\pi$
$383$	−9.85926e13	−	7.16317e13i	−0.611295	−	0.444132i	−0.849870	+	0.526992i	$0.823320\pi$
$384$	2.23954e13			0.136879
$385$	−2.50683e13	+	2.08348e13i	−0.151040	+	0.125532i
$386$	−1.42462e14			−0.846190
$387$	1.01292e12	+	7.35931e11i	0.00593152	+	0.00430950i
$388$	−3.65479e13	+	1.12483e14i	−0.211003	+	0.649400i
$389$	2.10546e13	+	6.47993e13i	0.119846	+	0.368848i	0.992927	−	0.118727i	$-0.0378814\pi$
$389$	2.10546e13	+	6.47993e13i	0.119846	+	0.368848i	−0.873081	+	0.487575i	$0.837881\pi$
$390$	−6.82803e12	+	4.96085e12i	−0.0383213	+	0.0278420i
$391$	4.89005e13	−	3.55283e13i	0.270608	−	0.196608i
$392$	8.35385e12	+	2.57105e13i	0.0455841	+	0.140293i
$393$	−2.64498e13	+	8.14040e13i	−0.142319	+	0.438013i
$394$	2.24073e13	+	1.62799e13i	0.118894	+	0.0863818i
$395$	−2.86838e13			−0.150090
$396$	−1.14552e14	−	7.23305e13i	−0.591122	−	0.373249i
$397$	2.08698e14			1.06211			0.531057	−	0.847336i	$-0.321795\pi$
$397$	2.08698e14			1.06211			0.531057	+	0.847336i	$0.321795\pi$
$398$	2.86528e12	+	2.08175e12i	0.0143817	+	0.0104489i
$399$	−1.30949e13	+	4.03021e13i	−0.0648265	+	0.199515i
$400$	−1.53911e13	−	4.73688e13i	−0.0751517	−	0.231293i
$401$	1.82587e14	−	1.32657e14i	0.879377	−	0.638905i	−0.0537097	−	0.998557i	$-0.517105\pi$
$401$	1.82587e14	−	1.32657e14i	0.879377	−	0.638905i	0.933087	+	0.359652i	$0.117105\pi$
$402$	1.38665e13	−	1.00746e13i	0.0658754	−	0.0478613i
$403$	1.84020e13	+	5.66356e13i	0.0862358	+	0.265406i
$404$	−3.21571e13	+	9.89694e13i	−0.148655	+	0.457513i
$405$	−1.29721e13	−	9.42478e12i	−0.0591572	−	0.0429802i
$406$	−2.68147e14			−1.20637
$407$	−3.31586e14	+	2.16213e13i	−1.47173	+	0.0959648i
$408$	3.39329e13			0.148590
$409$	−2.27989e14	−	1.65644e14i	−0.984998	−	0.715643i	−0.0261778	−	0.999657i	$-0.508334\pi$
$409$	−2.27989e14	−	1.65644e14i	−0.984998	−	0.715643i	−0.958820	+	0.284015i	$0.908334\pi$
$410$	4.19409e12	−	1.29081e13i	0.0178783	−	0.0550238i
$411$	−2.54287e13	−	7.82616e13i	−0.106953	−	0.329169i
$412$	3.06061e13	−	2.22366e13i	0.127020	−	0.0922857i
$413$	−4.06436e14	+	2.95293e14i	−1.66444	+	1.20928i
$414$	−9.31815e13	−	2.86783e14i	−0.376554	−	1.15892i
$415$	9.47025e12	−	2.91464e13i	0.0377656	−	0.116231i
$416$	9.52881e12	+	6.92308e12i	0.0374995	+	0.0272450i
$417$	4.65812e14			1.80910
$418$	7.77233e12	+	1.95005e13i	0.0297908	+	0.0747442i
$419$	−2.39303e14			−0.905257			−0.452628	−	0.891699i	$-0.649514\pi$
$419$	−2.39303e14			−0.905257			−0.452628	+	0.891699i	$0.649514\pi$
$420$	−3.29514e13	−	2.39406e13i	−0.123028	−	0.0893848i
$421$	8.41753e12	−	2.59065e13i	0.0310194	−	0.0954678i	−0.934348	−	0.356361i	$-0.884017\pi$
$421$	8.41753e12	−	2.59065e13i	0.0310194	−	0.0954678i	0.965368	+	0.260894i	$0.0840172\pi$
$422$	9.11167e13	+	2.80428e14i	0.331420	+	1.02001i
$423$	−4.25689e14	+	3.09281e14i	−1.52834	+	1.11040i
$424$	1.44546e13	−	1.05019e13i	0.0512264	−	0.0372182i
$425$	−2.33201e13	−	7.17718e13i	−0.0815813	−	0.251081i
$426$	−1.68091e14	+	5.17330e14i	−0.580484	+	1.78655i
$427$	5.34492e14	+	3.88331e14i	1.82216	+	1.32388i
$428$	−1.85811e14			−0.625361
$429$	−4.52470e13	−	1.13523e14i	−0.150340	−	0.377199i
$430$	1.86472e11			0.000611697
$431$	6.00953e13	+	4.36618e13i	0.194633	+	0.141409i	0.680834	−	0.732438i	$-0.261618\pi$
$431$	6.00953e13	+	4.36618e13i	0.194633	+	0.141409i	−0.486201	+	0.873847i	$0.661618\pi$
$432$	1.48979e13	−	4.58511e13i	0.0476393	−	0.146619i
$433$	4.99600e13	+	1.53761e14i	0.157739	+	0.485471i	0.998428	−	0.0560474i	$-0.0178498\pi$
$433$	4.99600e13	+	1.53761e14i	0.157739	+	0.485471i	−0.840689	+	0.541518i	$0.817850\pi$
$434$	−2.32498e14	+	1.68920e14i	−0.724812	+	0.526607i
$435$	9.62229e13	−	6.99100e13i	0.296202	−	0.215203i
$436$	−3.10960e13	−	9.57035e13i	−0.0945210	−	0.290906i
$437$	−1.44387e13	+	4.44378e13i	−0.0433392	+	0.133384i
$438$	4.12797e14	+	2.99914e14i	1.22357	+	0.888975i
$439$	4.47679e14			1.31042			0.655212	−	0.755445i	$-0.272579\pi$
$439$	4.47679e14			1.31042			0.655212	+	0.755445i	$0.272579\pi$
$440$	−2.01343e13	+	1.31287e12i	−0.0582031	+	0.00379517i
$441$	2.04342e14			0.583371
$442$	1.44378e13	+	1.04896e13i	0.0407078	+	0.0295759i
$443$	5.50588e13	−	1.69454e14i	0.153323	−	0.471879i	−0.844664	−	0.535296i	$-0.820200\pi$
$443$	5.50588e13	−	1.69454e14i	0.153323	−	0.471879i	0.997987	+	0.0634175i	$0.0202000\pi$
$444$	−1.28307e14	−	3.94887e14i	−0.352893	−	1.08609i
$445$	1.75904e13	−	1.27802e13i	0.0477855	−	0.0347182i
$446$	−4.68268e13	+	3.40217e13i	−0.125647	+	0.0912880i
$447$	−3.18372e14	−	9.79849e14i	−0.843808	−	2.59697i
$448$	−1.75647e13	+	5.40587e13i	−0.0459846	+	0.141526i
$449$	−1.63524e14	−	1.18807e14i	−0.422890	−	0.307248i	0.355909	−	0.934520i	$-0.384171\pi$
$449$	−1.63524e14	−	1.18807e14i	−0.422890	−	0.307248i	−0.778800	+	0.627273i	$0.784171\pi$
$450$	−3.76478e14			−0.961768
$451$	1.66171e14	+	1.04925e14i	0.419358	+	0.264793i
$452$	3.97388e14			0.990725
$453$	−3.12265e13	−	2.26874e13i	−0.0769100	−	0.0558784i
$454$	6.60850e13	−	2.03389e14i	0.160804	−	0.494902i
$455$	−6.61942e12	−	2.03725e13i	−0.0159132	−	0.0489758i
$456$	−2.12212e13	+	1.54181e13i	−0.0504037	+	0.0366204i
$457$	−5.71765e14	+	4.15412e14i	−1.34177	+	0.974854i	−0.342394	+	0.939556i	$0.611238\pi$
$457$	−5.71765e14	+	4.15412e14i	−1.34177	+	0.974854i	−0.999377	+	0.0352976i	$0.988762\pi$
$458$	−9.10399e13	−	2.80192e14i	−0.211092	−	0.649674i
$459$	2.25729e13	−	6.94722e13i	0.0517151	−	0.159163i
$460$	−3.63328e13	−	2.63974e13i	−0.0822491	−	0.0597575i
$461$	1.50057e14			0.335661			0.167831	−	0.985816i	$-0.446324\pi$
$461$	1.50057e14			0.335661			0.167831	+	0.985816i	$0.446324\pi$
$462$	4.53563e14	−	3.76966e14i	1.00255	−	0.833242i
$463$	2.16347e14			0.472559			0.236280	−	0.971685i	$-0.424072\pi$
$463$	2.16347e14			0.472559			0.236280	+	0.971685i	$0.424072\pi$
$464$	−1.34283e14	−	9.75624e13i	−0.289850	−	0.210588i
$465$	3.93905e13	−	1.21231e14i	0.0840233	−	0.258597i
$466$	−8.38947e13	−	2.58201e14i	−0.176853	−	0.544297i
$467$	−2.07898e14	+	1.51047e14i	−0.433119	+	0.314679i	−0.782895	−	0.622154i	$-0.786258\pi$
$467$	−2.07898e14	+	1.51047e14i	−0.433119	+	0.314679i	0.349776	+	0.936833i	$0.386258\pi$
$468$	7.20263e13	−	5.23302e13i	0.148299	−	0.107746i
$469$	1.34428e13	+	4.13728e13i	0.0273552	+	0.0841908i
$470$	−2.42165e13	+	7.45307e13i	−0.0487049	+	0.149898i
$471$	7.80910e13	+	5.67364e13i	0.155234	+	0.112784i
$472$	−3.10975e14			−0.611005
$473$	−6.65512e11	+	2.61677e12i	−0.00129247	+	0.00508194i
$474$	5.18979e14			0.996250
$475$	4.71950e13	+	3.42892e13i	0.0895532	+	0.0650642i
$476$	−2.66135e13	+	8.19081e13i	−0.0499188	+	0.153634i
$477$	−4.17334e13	−	1.28442e14i	−0.0773807	−	0.238153i
$478$	2.73693e14	−	1.98849e14i	0.501660	−	0.364478i
$479$	2.50805e14	−	1.82220e14i	0.454454	−	0.330180i	−0.336898	−	0.941541i	$-0.609378\pi$
$479$	2.50805e14	−	1.82220e14i	0.454454	−	0.330180i	0.791352	+	0.611361i	$0.209378\pi$
$480$	−7.79093e12	−	2.39780e13i	−0.0139560	−	0.0429523i
$481$	6.74794e13	−	2.07680e14i	0.119501	−	0.367787i
$482$	2.69526e14	+	1.95822e14i	0.471892	+	0.342850i
$483$	1.31269e15			2.27224
$484$	5.34350e13	−	2.87231e14i	0.0914485	−	0.491566i
$485$	1.33146e14			0.225293
$486$	4.45560e14	+	3.23719e14i	0.745430	+	0.541587i
$487$	−5.90769e13	+	1.81820e14i	−0.0977256	+	0.300768i	−0.987954	−	0.154745i	$-0.950544\pi$
$487$	−5.90769e13	+	1.81820e14i	−0.0977256	+	0.300768i	0.890229	+	0.455514i	$0.150544\pi$
$488$	1.26374e14	+	3.88938e14i	0.206703	+	0.636167i
$489$	−1.20409e15	+	8.74819e14i	−1.94742	+	1.41488i
$490$	2.46212e13	−	1.78884e13i	0.0393759	−	0.0286083i
$491$	2.22686e14	+	6.85358e14i	0.352164	+	1.08385i	0.957635	+	0.287983i	$0.0929847\pi$
$491$	2.22686e14	+	6.85358e14i	0.352164	+	1.08385i	−0.605471	+	0.795867i	$0.707015\pi$
$492$	−7.58840e13	+	2.33547e14i	−0.118670	+	0.365230i
$493$	−2.03462e14	−	1.47824e14i	−0.314648	−	0.228605i
$494$	−1.37954e13			−0.0210977
$495$	−3.75916e13	+	1.47809e14i	−0.0568541	+	0.223548i
$496$	−1.77890e14			−0.266074
$497$	−1.11691e15	−	8.11484e14i	−1.65218	−	1.20038i
$498$	−1.71346e14	+	5.27348e14i	−0.250676	+	0.771501i
$499$	2.86152e14	+	8.80686e14i	0.414042	+	1.27429i	0.913105	+	0.407724i	$0.133678\pi$
$499$	2.86152e14	+	8.80686e14i	0.414042	+	1.27429i	−0.499063	+	0.866566i	$0.666322\pi$
$500$	−9.19929e13	+	6.68368e13i	−0.131650	+	0.0956490i
$501$	6.96215e14	−	5.05830e14i	0.985453	−	0.715974i
$502$	3.50041e13	+	1.07732e14i	0.0490059	+	0.150825i
$503$	2.29029e14	−	7.04879e14i	0.317151	−	0.976092i	−0.657708	−	0.753273i	$-0.728474\pi$
$503$	2.29029e14	−	7.04879e14i	0.317151	−	0.976092i	0.974860	−	0.222819i	$-0.0715259\pi$
$504$	3.47592e14	+	2.52540e14i	0.476104	+	0.345910i
$505$	1.17150e14			0.158723
$506$	5.00107e14	−	4.15650e14i	0.670247	−	0.557057i
$507$	−1.08781e15			−1.44214
$508$	−9.12001e13	−	6.62607e13i	−0.119604	−	0.0868972i
$509$	1.84750e14	−	5.68603e14i	0.239683	−	0.737669i	−0.756782	−	0.653667i	$-0.773230\pi$
$509$	1.84750e14	−	5.68603e14i	0.239683	−	0.737669i	0.996466	−	0.0840020i	$-0.0267702\pi$
$510$	−1.18046e13	−	3.63307e13i	−0.0151501	−	0.0466271i
$511$	−1.04770e15	+	7.61197e14i	−1.33021	+	0.966457i
$512$	−2.84648e13	+	2.06809e13i	−0.0357538	+	0.0259767i
$513$	1.74493e13	+	5.37034e13i	0.0216837	+	0.0667354i
$514$	−5.37908e13	+	1.65551e14i	−0.0661318	+	0.203533i
$515$	−3.44553e13	−	2.50332e13i	−0.0419098	−	0.0304493i
$516$	−3.37384e12			−0.00406024
$517$	−9.59467e14	−	6.05830e14i	−1.14244	−	0.721361i
$518$	1.05382e15			1.24152
$519$	−1.69170e15	−	1.22909e15i	−1.97198	−	1.43273i
$520$	4.09742e12	−	1.26106e13i	0.00472598	−	0.0145451i
$521$	2.61233e14	+	8.03992e14i	0.298140	+	0.917581i	0.982149	+	0.188107i	$0.0602352\pi$
$521$	2.61233e14	+	8.03992e14i	0.298140	+	0.917581i	−0.684008	+	0.729474i	$0.739765\pi$
$522$	−1.01502e15	+	7.37455e14i	−1.14627	+	0.832814i
$523$	1.02703e15	−	7.46178e14i	1.14768	−	0.833841i	0.159512	−	0.987196i	$-0.449008\pi$
$523$	1.02703e15	−	7.46178e14i	1.14768	−	0.833841i	0.988171	+	0.153355i	$0.0490079\pi$
$524$	−4.15539e13	−	1.27890e14i	−0.0459505	−	0.141421i
$525$	5.06451e14	−	1.55870e15i	0.554194	−	1.70563i
$526$	−7.11002e14	−	5.16573e14i	−0.769927	−	0.559385i
$527$	−2.69534e14			−0.288838
$528$	3.64291e14	−	2.37538e13i	0.386333	−	0.0251911i
$529$	4.94592e14			0.519088
$530$	−1.62725e13	−	1.18226e13i	−0.0169019	−	0.0122800i
$531$	−7.26375e14	+	2.23555e15i	−0.746691	+	2.29808i
$532$	−2.05728e13	−	6.33166e13i	−0.0209305	−	0.0644175i
$533$	−1.04483e14	+	7.59116e13i	−0.105208	+	0.0764378i
$534$	−3.18265e14	+	2.31233e14i	−0.317184	+	0.230448i
$535$	6.46400e13	+	1.98942e14i	0.0637611	+	0.196236i
$536$	−8.32112e12	+	2.56098e13i	−0.00812410	+	0.0250034i
$537$	−8.07188e14	−	5.86456e14i	−0.780039	−	0.566731i
$538$	−8.37045e14			−0.800657
$539$	1.63156e14	+	4.09354e14i	0.154477	+	0.387580i
$540$	−5.42739e13			−0.0508657
$541$	−4.71684e14	−	3.42698e14i	−0.437589	−	0.317927i	0.347087	−	0.937833i	$-0.387171\pi$
$541$	−4.71684e14	−	3.42698e14i	−0.437589	−	0.317927i	−0.784676	+	0.619906i	$0.787171\pi$
$542$	3.70779e14	−	1.14114e15i	0.340501	−	1.04796i
$543$	6.19821e14	+	1.90761e15i	0.563465	+	1.73417i
$544$	−4.31289e13	+	3.13350e13i	−0.0388128	+	0.0281991i
$545$	−9.16488e13	+	6.65867e13i	−0.0816481	+	0.0593208i
$546$	1.19766e14	+	3.68601e14i	0.105626	+	0.325085i
$547$	−6.73913e13	+	2.07409e14i	−0.0588401	+	0.181091i	−0.976157	−	0.217068i	$-0.930351\pi$
$547$	−6.73913e13	+	2.07409e14i	−0.0588401	+	0.181091i	0.917316	+	0.398159i	$0.130351\pi$
$548$	1.04590e14	+	7.59891e13i	0.0904060	+	0.0656838i
$549$	3.09120e15			2.64532
$550$	−3.00597e14	−	7.54191e14i	−0.254677	−	0.638979i
$551$	1.94409e14			0.163073
$552$	6.57373e14	+	4.77609e14i	0.545942	+	0.396650i
$553$	−4.07035e14	+	1.25272e15i	−0.334691	+	1.03007i
$554$	−2.31223e14	−	7.11632e14i	−0.188247	−	0.579365i
$555$	−3.78157e14	+	2.74747e14i	−0.304832	+	0.221473i
$556$	−5.92051e14	+	4.30150e14i	−0.472550	+	0.343327i
$557$	8.92710e13	+	2.74748e14i	0.0705516	+	0.217135i	0.980115	−	0.198429i	$-0.0635840\pi$
$557$	8.92710e13	+	2.74748e14i	0.0705516	+	0.217135i	−0.909564	+	0.415565i	$0.863584\pi$
$558$	−4.15515e14	+	1.27882e15i	−0.325161	+	1.00074i
$559$	−1.43550e12	−	1.04295e12i	−0.00111234	−	0.000808166i
$560$	6.39892e13			0.0490990
$561$	5.51962e14	−	3.59910e13i	0.419385	−	0.0273463i
$562$	1.97112e14			0.148308
$563$	1.81003e15	+	1.31506e15i	1.34862	+	0.979830i	0.999079	+	0.0429090i	$0.0136626\pi$
$563$	1.81003e15	+	1.31506e15i	1.34862	+	0.979830i	0.349541	+	0.936921i	$0.386337\pi$
$564$	4.38151e14	−	1.34849e15i	0.323287	−	0.994975i
$565$	−1.38243e14	−	4.25469e14i	−0.101013	−	0.310886i
$566$	−6.87811e14	+	4.99724e14i	−0.497713	+	0.361610i
$567$	−5.95693e14	+	4.32796e14i	−0.426889	+	0.310153i
$568$	−2.64079e14	−	8.12752e14i	−0.187421	−	0.576822i
$569$	2.85289e14	−	8.78028e14i	0.200524	−	0.617151i	−0.799343	−	0.600875i	$-0.794819\pi$
$569$	2.85289e14	−	8.78028e14i	0.200524	−	0.617151i	0.999868	−	0.0162758i	$-0.00518097\pi$
$570$	2.38900e13	+	1.73571e13i	0.0166305	+	0.0120828i
$571$	−1.20215e15			−0.828820			−0.414410	−	0.910090i	$-0.636012\pi$
$571$	−1.20215e15			−0.828820			−0.414410	+	0.910090i	$0.636012\pi$
$572$	1.62341e14	+	1.02506e14i	0.110854	+	0.0699957i
$573$	2.54478e15			1.72108
$574$	−5.04226e14	−	3.66342e14i	−0.337761	−	0.245398i
$575$	5.58423e14	−	1.71865e15i	0.370502	−	1.14029i
$576$	8.21836e13	+	2.52935e14i	0.0540084	+	0.166221i
$577$	9.37467e14	−	6.81109e14i	0.610223	−	0.443353i	−0.239270	−	0.970953i	$-0.576908\pi$
$577$	9.37467e14	−	6.81109e14i	0.610223	−	0.443353i	0.849493	+	0.527600i	$0.176908\pi$
$578$	8.21902e14	−	5.97147e14i	0.529928	−	0.385015i
$579$	−8.96685e14	−	2.75971e15i	−0.572674	−	1.76251i
$580$	−5.77422e13	+	1.77712e14i	−0.0365292	+	0.112425i
$581$	−1.13854e15	−	8.27199e14i	−0.713477	−	0.518372i
$582$	−2.40902e15			−1.49542
$583$	2.23984e14	−	1.86158e14i	0.137734	−	0.114473i
$584$	−8.01621e14			−0.488313
$585$	−8.10847e13	−	5.89115e13i	−0.0489307	−	0.0355502i
$586$	2.25992e14	−	6.95532e14i	0.135100	−	0.415796i
$587$	6.57079e14	+	2.02228e15i	0.389142	+	1.19766i	0.933431	+	0.358758i	$0.116800\pi$
$587$	6.57079e14	+	2.02228e15i	0.389142	+	1.19766i	−0.544289	+	0.838898i	$0.683200\pi$
$588$	−4.45473e14	+	3.23655e14i	−0.261364	+	0.189892i
$589$	1.68563e14	−	1.22468e14i	0.0979778	−	0.0711850i
$590$	1.08182e14	+	3.32950e14i	0.0622973	+	0.191731i
$591$	−1.74331e14	+	5.36536e14i	−0.0994589	+	0.306103i
$592$	5.27734e14	+	3.83421e14i	0.298295	+	0.216724i
$593$	3.54366e14			0.198450			0.0992250	−	0.995065i	$-0.468364\pi$
$593$	3.54366e14			0.198450			0.0992250	+	0.995065i	$0.468364\pi$
$594$	1.93702e14	−	7.61629e14i	0.107475	−	0.422589i
$595$	9.69544e13			0.0532997
$596$	1.30949e15	+	9.51397e14i	0.713258	+	0.518212i
$597$	−2.22922e13	+	6.86082e13i	−0.0120308	+	0.0370269i
$598$	1.32056e14	+	4.06426e14i	0.0706157	+	0.217333i
$599$	1.87227e15	−	1.36028e15i	0.992021	−	0.720745i	0.0316580	−	0.999499i	$-0.489921\pi$
$599$	1.87227e15	−	1.36028e15i	0.992021	−	0.720745i	0.960363	+	0.278754i	$0.0899213\pi$
$600$	8.20736e14	−	5.96300e14i	0.430895	−	0.313064i
$601$	1.17680e14	+	3.62181e14i	0.0612198	+	0.188415i	0.976989	−	0.213290i	$-0.0684178\pi$
$601$	1.17680e14	+	3.62181e14i	0.0612198	+	0.188415i	−0.915769	+	0.401705i	$0.868418\pi$
$602$	2.64611e12	−	8.14388e12i	0.00136404	−	0.00419808i
$603$	1.64668e14	+	1.19638e14i	0.0841133	+	0.0611119i
$604$	6.06395e13			0.0306939
$605$	−3.26117e14	+	4.27109e13i	−0.163576	+	0.0214232i
$606$	−2.11960e15			−1.05355
$607$	6.34687e14	+	4.61127e14i	0.312624	+	0.227135i	0.733022	−	0.680205i	$-0.238109\pi$
$607$	6.34687e14	+	4.61127e14i	0.312624	+	0.227135i	−0.420398	+	0.907340i	$0.638109\pi$
$608$	1.27346e13	−	3.91930e13i	0.00621605	−	0.0191310i
$609$	−1.68778e15	−	5.19445e15i	−0.816433	−	2.51272i
$610$	3.72459e14	−	2.70607e14i	0.178552	−	0.129726i
$611$	6.03282e14	−	4.38310e14i	0.286612	−	0.208235i
$612$	1.24522e14	+	3.83239e14i	0.0586291	+	0.180442i
$613$	−1.00543e15	+	3.09439e15i	−0.469157	+	1.44392i	0.384522	+	0.923116i	$0.374366\pi$
$613$	−1.00543e15	+	3.09439e15i	−0.469157	+	1.44392i	−0.853679	+	0.520800i	$0.825634\pi$
$614$	2.26437e15	+	1.64516e15i	1.04718	+	0.760821i
$615$	2.76449e14			0.126707
$616$	−2.28376e14	+	8.97965e14i	−0.103742	+	0.407911i
$617$	1.66732e15			0.750673			0.375336	−	0.926889i	$-0.377527\pi$
$617$	1.66732e15			0.750673			0.375336	+	0.926889i	$0.377527\pi$
$618$	6.23401e14	+	4.52928e14i	0.278183	+	0.202112i
$619$	−1.19046e13	+	3.66385e13i	−0.00526521	+	0.0162046i	−0.953655	−	0.300903i	$-0.902712\pi$
$619$	−1.19046e13	+	3.66385e13i	−0.00526521	+	0.0162046i	0.948389	+	0.317108i	$0.102712\pi$
$620$	6.18845e13	+	1.90461e14i	0.0271286	+	0.0834932i
$621$	1.41513e15	−	1.02815e15i	0.614882	−	0.446738i
$622$	4.12660e14	−	2.99815e14i	0.177724	−	0.129124i
$623$	−3.08541e14	−	9.49592e14i	−0.131713	−	0.405371i
$624$	−7.41349e13	+	2.28164e14i	−0.0313695	+	0.0965454i
$625$	−1.77279e15	−	1.28801e15i	−0.743562	−	0.540229i
$626$	2.98584e14			0.124139
$627$	−3.28836e14	+	2.73303e14i	−0.135522	+	0.112635i
$628$	−1.51647e14			−0.0619521
$629$	7.99606e14	+	5.80948e14i	0.323815	+	0.235266i
$630$	1.49466e14	−	4.60008e14i	0.0600024	−	0.184668i
$631$	1.17742e15	+	3.62373e15i	0.468565	+	1.44210i	0.854443	+	0.519546i	$0.173899\pi$
$631$	1.17742e15	+	3.62373e15i	0.468565	+	1.44210i	−0.385877	+	0.922550i	$0.626101\pi$
$632$	−6.59626e14	+	4.79246e14i	−0.260228	+	0.189067i
$633$	−4.85884e15	+	3.53015e15i	−1.90026	+	1.38062i
$634$	5.99559e14	+	1.84525e15i	0.232456	+	0.715426i
$635$	−3.92164e13	+	1.20696e14i	−0.0150734	+	0.0463912i
$636$	2.94419e14	+	2.13908e14i	0.112189	+	0.0815103i
$637$	−2.89591e14			−0.109400
$638$	−2.28777e15	−	1.44455e15i	−0.856838	−	0.541027i
$639$	−6.45958e15			−2.39855
$640$	3.20446e13	+	2.32818e13i	0.0117968	+	0.00857089i
$641$	−1.46620e15	+	4.51251e15i	−0.535150	+	1.64702i	0.208176	+	0.978091i	$0.433247\pi$
$641$	−1.46620e15	+	4.51251e15i	−0.535150	+	1.64702i	−0.743326	+	0.668930i	$0.766753\pi$
$642$	−1.16954e15	−	3.59946e15i	−0.423225	−	1.30255i
$643$	3.21367e15	−	2.33487e15i	1.15303	−	0.837726i	0.164149	−	0.986435i	$-0.447512\pi$
$643$	3.21367e15	−	2.33487e15i	1.15303	−	0.837726i	0.988881	+	0.148710i	$0.0475121\pi$
$644$	−1.66844e15	+	1.21220e15i	−0.593525	+	0.431221i
$645$	1.17369e12	+	3.61226e12i	0.000413977	+	0.00127409i
$646$	1.92950e13	−	5.93840e13i	0.00674787	−	0.0207678i
$647$	3.12385e15	+	2.26961e15i	1.08322	+	0.787006i	0.978242	−	0.207468i	$-0.0665224\pi$
$647$	3.12385e15	+	2.26961e15i	1.08322	+	0.787006i	0.104979	+	0.994474i	$0.466522\pi$
$648$	−4.55780e14			−0.156709
$649$	−5.05841e15	+	3.29837e14i	−1.72452	+	0.112448i
$650$	5.33541e14			0.180362
$651$	−4.73564e15	−	3.44064e15i	−1.58739	−	1.15331i
$652$	7.22558e14	−	2.22380e15i	0.240166	−	0.739154i
$653$	−3.56475e14	−	1.09712e15i	−0.117492	−	0.361602i	0.874967	−	0.484183i	$-0.160883\pi$
$653$	−3.56475e14	−	1.09712e15i	−0.117492	−	0.361602i	−0.992459	+	0.122581i	$0.960883\pi$
$654$	1.65821e15	−	1.20476e15i	0.541953	−	0.393752i
$655$	−1.22471e14	+	8.89807e13i	−0.0396924	+	0.0288382i
$656$	−1.19218e14	−	3.66914e14i	−0.0383151	−	0.117922i
$657$	−1.87242e15	+	5.76273e15i	−0.596753	+	1.83662i
$658$	2.91138e15	+	2.11524e15i	0.920145	+	0.668525i
$659$	3.30782e14			0.103675			0.0518373	−	0.998656i	$-0.483492\pi$
$659$	3.30782e14			0.103675			0.0518373	+	0.998656i	$0.483492\pi$
$660$	−1.52162e14	−	3.81770e14i	−0.0472949	−	0.118661i
$661$	9.01561e14			0.277899			0.138950	−	0.990299i	$-0.455627\pi$
$661$	9.01561e14			0.277899			0.138950	+	0.990299i	$0.455627\pi$
$662$	−8.05944e14	−	5.85552e14i	−0.246369	−	0.178997i
$663$	−1.12327e14	+	3.45707e14i	−0.0340533	+	0.104805i
$664$	−2.69193e14	−	8.28492e14i	−0.0809356	−	0.249094i
$665$	−6.06340e13	+	4.40532e13i	−0.0180800	+	0.0131359i
$666$	3.98904e15	−	2.89820e15i	1.17967	−	0.857079i
$667$	−1.86098e15	−	5.72750e15i	−0.545819	−	1.67986i
$668$	−4.17791e14	+	1.28583e15i	−0.121531	+	0.374035i
$669$	−9.53793e14	−	6.92971e14i	−0.275176	−	0.199927i
$670$	3.03142e13			0.00867431
$671$	2.46816e15	+	6.19253e15i	0.700485	+	1.75750i
$672$	−1.15776e15			−0.325903
$673$	3.77581e15	+	2.74329e15i	1.05421	+	0.765928i	0.973008	−	0.230769i	$-0.0741243\pi$
$673$	3.77581e15	+	2.74329e15i	1.05421	+	0.765928i	0.0812014	+	0.996698i	$0.474124\pi$
$674$	1.09795e14	−	3.37914e14i	0.0304055	−	0.0935786i
$675$	−6.74858e14	−	2.07700e15i	−0.185371	−	0.570513i
$676$	1.38261e15	−	1.00453e15i	0.376698	−	0.273687i
$677$	−1.36409e15	+	9.91071e14i	−0.368643	+	0.267835i	−0.756648	−	0.653822i	$-0.773164\pi$
$677$	−1.36409e15	+	9.91071e14i	−0.368643	+	0.267835i	0.388005	+	0.921657i	$0.373164\pi$
$678$	2.50125e15	+	7.69804e15i	0.670491	+	2.06356i
$679$	1.88939e15	−	5.81496e15i	0.502387	−	1.54619i
$680$	4.85530e13	+	3.52758e13i	0.0128061	+	0.00930418i
$681$	4.35592e15			1.13965
$682$	−2.89361e15	+	1.88680e14i	−0.750976	+	0.0489679i
$683$	−4.97310e15			−1.28031			−0.640153	−	0.768248i	$-0.721129\pi$
$683$	−4.97310e15			−1.28031			−0.640153	+	0.768248i	$0.721129\pi$
$684$	−2.52007e14	−	1.83094e14i	−0.0643582	−	0.0467590i
$685$	4.49741e13	−	1.38416e14i	0.0113937	−	0.0350662i
$686$	6.03208e14	+	1.85648e15i	0.151595	+	0.466561i
$687$	4.85475e15	−	3.52718e15i	1.21033	−	0.879358i
$688$	4.28818e12	−	3.11555e12i	0.00106056	−	0.000770545i
$689$	5.91442e13	+	1.82027e14i	0.0145113	+	0.0446612i
$690$	2.82673e14	−	8.69977e14i	0.0688040	−	0.211757i
$691$	−5.04918e15	−	3.66844e15i	−1.21925	−	0.885834i	−0.223209	−	0.974771i	$-0.571653\pi$
$691$	−5.04918e15	−	3.66844e15i	−1.21925	−	0.885834i	−0.996037	+	0.0889365i	$0.971653\pi$
$692$	3.28516e15			0.786997
$693$	5.92189e15	+	3.73922e15i	1.40743	+	0.888686i
$694$	−1.58025e15			−0.372606
$695$	6.66509e14	+	4.84247e14i	0.155916	+	0.113279i
$696$	1.04473e15	−	3.21536e15i	0.242468	−	0.746241i
$697$	−1.80635e14	−	5.55937e14i	−0.0415931	−	0.128010i
$698$	−1.09653e15	+	7.96677e14i	−0.250505	+	0.182003i
$699$	4.47372e15	−	3.25035e15i	1.01402	−	0.736726i
$700$	7.95661e14	+	2.44879e15i	0.178932	+	0.550697i
$701$	2.30481e15	−	7.09346e15i	0.514263	−	1.58274i	−0.270356	−	0.962760i	$-0.587142\pi$
$701$	2.30481e15	−	7.09346e15i	0.514263	−	1.58274i	0.784619	−	0.619978i	$-0.212858\pi$
$702$	4.17813e14	+	3.03559e14i	0.0924971	+	0.0672031i
$703$	−7.64029e14			−0.167824
$704$	−4.41081e14	+	3.66592e14i	−0.0961321	+	0.0798975i
$705$	−1.59620e15			−0.345182
$706$	4.19020e15	+	3.04436e15i	0.899102	+	0.653236i
$707$	1.66240e15	−	5.11635e15i	0.353940	−	1.08932i
$708$	−1.95734e15	−	6.02409e15i	−0.413508	−	1.27265i
$709$	4.99806e15	−	3.63130e15i	1.04772	−	0.761216i	0.0759458	−	0.997112i	$-0.475802\pi$
$709$	4.99806e15	−	3.63130e15i	1.04772	−	0.761216i	0.971778	+	0.235896i	$0.0758024\pi$
$710$	−7.78317e14	+	5.65480e14i	−0.161896	+	0.117624i
$711$	1.90447e15	+	5.86137e15i	0.393090	+	1.20981i
$712$	1.90987e14	−	5.87797e14i	0.0391168	−	0.120389i
$713$	−5.22161e15	−	3.79372e15i	−1.06124	−	0.771033i
$714$	−1.75420e15			−0.353785
$715$	5.32744e13	−	2.09473e14i	0.0106619	−	0.0419223i
$716$	1.56750e15			0.311305
$717$	5.57472e15	+	4.05027e15i	1.09867	+	0.798231i
$718$	−1.76076e15	+	5.41905e15i	−0.344362	+	1.05984i
$719$	−9.38429e14	−	2.88819e15i	−0.182135	−	0.560553i	0.817753	−	0.575570i	$-0.195220\pi$
$719$	−9.38429e14	−	2.88819e15i	−0.182135	−	0.560553i	−0.999887	+	0.0150172i	$0.995220\pi$
$720$	2.42219e14	−	1.75982e14i	0.0466529	−	0.0338953i
$721$	−1.58222e15	+	1.14955e15i	−0.302429	+	0.219728i
$722$	−1.13700e15	−	3.49934e15i	−0.215679	−	0.663791i
$723$	−2.09694e15	+	6.45371e15i	−0.394753	+	1.21492i
$724$	−2.54936e15	−	1.85222e15i	−0.476288	−	0.346043i
$725$	−7.51883e15			−1.39409
$726$	5.90046e15	−	7.72772e14i	1.08576	−	0.142200i
$727$	3.24820e15			0.593203			0.296602	−	0.955001i	$-0.404147\pi$
$727$	3.24820e15			0.593203			0.296602	+	0.955001i	$0.404147\pi$
$728$	−4.92604e14	−	3.57898e14i	−0.0892844	−	0.0648689i
$729$	−2.70508e15	+	8.32539e15i	−0.486608	+	1.49763i
$730$	2.78868e14	+	8.58268e14i	0.0497878	+	0.153231i
$731$	6.49732e12	−	4.72058e12i	0.00115130	−	0.000836469i
$732$	−6.73893e15	+	4.89612e15i	−1.18517	+	0.861075i
$733$	5.56936e14	+	1.71407e15i	0.0972150	+	0.299197i	0.987825	−	0.155572i	$-0.0497219\pi$
$733$	5.56936e14	+	1.71407e15i	0.0972150	+	0.299197i	−0.890610	+	0.454769i	$0.849722\pi$
$734$	1.26560e15	−	3.89510e15i	0.219264	−	0.674824i
$735$	5.01498e14	+	3.64359e14i	0.0862360	+	0.0626541i
$736$	−1.27657e15			−0.217880
$737$	−1.08191e14	+	4.25402e14i	−0.0183281	+	0.0720656i
$738$	−2.91616e15			−0.490344
$739$	−3.89130e15	−	2.82720e15i	−0.649457	−	0.471858i	0.213629	−	0.976915i	$-0.431472\pi$
$739$	−3.89130e15	−	2.82720e15i	−0.649457	−	0.471858i	−0.863086	+	0.505057i	$0.831472\pi$
$740$	2.26928e14	−	6.98411e14i	0.0375935	−	0.115701i
$741$	−8.68310e13	−	2.67238e14i	−0.0142782	−	0.0439439i
$742$	−7.47249e14	+	5.42908e14i	−0.121967	+	0.0886146i
$743$	3.63154e15	−	2.63847e15i	0.588373	−	0.427478i	−0.253360	−	0.967372i	$-0.581536\pi$
$743$	3.63154e15	−	2.63847e15i	0.588373	−	0.427478i	0.841733	+	0.539894i	$0.181536\pi$
$744$	−1.11968e15	−	3.44602e15i	−0.180071	−	0.554200i
$745$	5.63084e14	−	1.73299e15i	0.0898904	−	0.276654i
$746$	−5.55263e15	−	4.03422e15i	−0.879903	−	0.639287i
$747$	−6.58468e15			−1.03579
$748$	−6.68312e14	+	5.55449e14i	−0.104357	+	0.0867332i
$749$	9.60575e15			1.48895
$750$	−1.87376e15	−	1.36137e15i	−0.288322	−	0.209478i
$751$	−7.97790e14	+	2.45535e15i	−0.121862	+	0.375053i	−0.993316	−	0.115424i	$-0.963177\pi$
$751$	−7.97790e14	+	2.45535e15i	−0.121862	+	0.375053i	0.871454	+	0.490477i	$0.163177\pi$
$752$	6.88357e14	+	2.11855e15i	0.104380	+	0.321248i
$753$	−1.86661e15	+	1.35617e15i	−0.280984	+	0.204147i
$754$	1.43848e15	−	1.04511e15i	0.214961	−	0.156179i
$755$	−2.10953e13	−	6.49246e13i	−0.00312952	−	0.00963166i
$756$	−7.70168e14	+	2.37033e15i	−0.113427	+	0.349092i
$757$	5.10938e15	+	3.71218e15i	0.747035	+	0.542752i	0.894906	−	0.446254i	$-0.147242\pi$
$757$	5.10938e15	+	3.71218e15i	0.747035	+	0.542752i	−0.147872	+	0.989007i	$0.547242\pi$
$758$	−8.37810e15			−1.21609
$759$	1.11996e16	+	7.07168e15i	1.61388	+	1.01904i
$760$	−4.63927e13			−0.00663704
$761$	3.67748e15	+	2.67185e15i	0.522318	+	0.379486i	0.817476	−	0.575962i	$-0.195372\pi$
$761$	3.67748e15	+	2.67185e15i	0.522318	+	0.379486i	−0.295159	+	0.955448i	$0.595372\pi$
$762$	7.09544e14	−	2.18375e15i	0.100052	−	0.307929i
$763$	1.60755e15	+	4.94752e15i	0.225050	+	0.692632i
$764$	−3.23444e15	+	2.34996e15i	−0.449558	+	0.326623i
$765$	3.67002e14	−	2.66643e14i	0.0506443	−	0.0367953i
$766$	1.20509e15	+	3.70888e15i	0.165105	+	0.508142i
$767$	1.02941e15	−	3.16820e15i	0.140028	−	0.430961i
$768$	−5.79785e14	−	4.21238e14i	−0.0783033	−	0.0568907i
$769$	−7.31996e15			−0.981554			−0.490777	−	0.871285i	$-0.663287\pi$
$769$	−7.31996e15			−0.981554			−0.490777	+	0.871285i	$0.663287\pi$
$770$	1.04087e15	−	6.78704e13i	0.138579	−	0.00903610i
$771$	−3.54556e15			−0.468690
$772$	3.68812e15	+	2.67958e15i	0.484073	+	0.351699i
$773$	−1.00880e14	+	3.10477e14i	−0.0131467	+	0.0404615i	−0.957415	−	0.288716i	$-0.906772\pi$
$773$	−1.00880e14	+	3.10477e14i	−0.0131467	+	0.0404615i	0.944268	+	0.329178i	$0.106772\pi$
$774$	−1.23809e13	−	3.81044e13i	−0.00160205	−	0.00493060i
$775$	−6.51923e15	+	4.73650e15i	−0.837600	+	0.608552i
$776$	3.06188e15	−	2.22459e15i	0.390615	−	0.283798i
$777$	6.63298e15	+	2.04142e16i	0.840220	+	2.58593i
$778$	6.73746e14	−	2.07358e15i	0.0847439	−	0.260815i
$779$	3.65568e14	+	2.65601e14i	0.0456575	+	0.0331721i
$780$	2.70077e14			0.0334940
$781$	−5.15763e15	−	1.29404e16i	−0.635140	−	1.59355i
$782$	−1.93422e15			−0.236520
$783$	−5.88796e15	−	4.27786e15i	−0.714950	−	0.519441i
$784$	2.67323e14	−	8.22736e14i	0.0322328	−	0.0992024i
$785$	5.27550e13	+	1.62363e14i	0.00631656	+	0.0194404i
$786$	2.21588e15	−	1.60993e15i	0.263465	−	0.191419i
$787$	5.95954e15	−	4.32986e15i	0.703642	−	0.511226i	−0.177474	−	0.984125i	$-0.556793\pi$
$787$	5.95954e15	−	4.32986e15i	0.703642	−	0.511226i	0.881116	+	0.472900i	$0.156793\pi$
$788$	−2.73883e14	−	8.42925e14i	−0.0321123	−	0.0988314i
$789$	5.53166e15	−	1.70247e16i	0.644068	−	1.98224i
$790$	7.42583e14	+	5.39518e14i	0.0858610	+	0.0623817i
$791$	−2.05435e16			−2.35887
$792$	1.60510e15	+	4.02715e15i	0.183026	+	0.459207i
$793$	−4.38081e15			−0.496081
$794$	−5.40289e15	−	3.92543e15i	−0.607594	−	0.441443i
$795$	1.26601e14	−	3.89638e14i	0.0141390	−	0.0435153i
$796$	−3.50221e13	−	1.07787e14i	−0.00388437	−	0.0119549i
$797$	7.29910e15	−	5.30310e15i	0.803986	−	0.584130i	−0.108095	−	0.994141i	$-0.534475\pi$
$797$	7.29910e15	−	5.30310e15i	0.803986	−	0.584130i	0.912081	+	0.410011i	$0.134475\pi$
$798$	1.09706e15	−	7.97058e14i	0.120009	−	0.0871914i
$799$	1.04298e15	+	3.20996e15i	0.113310	+	0.348732i
$800$	−4.92514e14	+	1.51580e15i	−0.0531403	+	0.163549i
$801$	−3.77948e15	−	2.74595e15i	−0.404998	−	0.294248i
$802$	−7.22207e15			−0.768604
$803$	−1.30394e16	+	8.50242e14i	−1.37823	+	0.0898684i
$804$	−5.48477e14			−0.0575772
$805$	1.87827e15	+	1.36465e15i	0.195831	+	0.142280i
$806$	5.88864e14	−	1.81234e15i	0.0609779	−	0.187671i
$807$	−5.26855e15	−	1.62149e16i	−0.541859	−	1.66767i
$808$	2.69403e15	−	1.95733e15i	0.275194	−	0.199940i
$809$	−1.20212e16	+	8.73392e15i	−1.21964	+	0.886120i	−0.996070	−	0.0885684i	$-0.971771\pi$
$809$	−1.20212e16	+	8.73392e15i	−1.21964	+	0.886120i	−0.223569	+	0.974688i	$0.571771\pi$
$810$	1.58557e14	+	4.87988e14i	0.0159778	+	0.0491746i
$811$	2.71387e15	−	8.35244e15i	0.271628	−	0.835985i	−0.718464	−	0.695564i	$-0.755154\pi$
$811$	2.71387e15	−	8.35244e15i	0.271628	−	0.835985i	0.990092	−	0.140421i	$-0.0448456\pi$
$812$	6.94194e15	+	5.04362e15i	0.690117	+	0.501400i
$813$	2.44395e16			2.41320
$814$	8.99095e15	+	5.67710e15i	0.881803	+	0.556791i
$815$	−2.63231e15			−0.256431
$816$	−8.78472e14	−	6.38247e14i	−0.0850026	−	0.0617580i
$817$	−1.91845e12	+	5.90438e12i	−0.000184386	+	0.000567483i
$818$	2.78669e15	+	8.57654e15i	0.266039	+	0.818783i
$819$	−3.72350e15	+	2.70528e15i	−0.353093	+	0.256537i
$820$	−3.51369e14	+	2.55284e14i	−0.0330969	+	0.0240463i
$821$	3.75860e15	+	1.15678e16i	0.351673	+	1.08234i	0.957914	+	0.287057i	$0.0926768\pi$
$821$	3.75860e15	+	1.15678e16i	0.351673	+	1.08234i	−0.606241	+	0.795281i	$0.707323\pi$
$822$	−8.13719e14	+	2.50437e15i	−0.0756275	+	0.232757i
$823$	2.46658e15	+	1.79208e15i	0.227718	+	0.165446i	0.695794	−	0.718242i	$-0.255053\pi$
$823$	2.46658e15	+	1.79208e15i	0.227718	+	0.165446i	−0.468076	+	0.883688i	$0.655053\pi$
$824$	−1.21060e15			−0.111020
$825$	1.27179e16	−	1.05701e16i	1.15856	−	0.962903i
$826$	1.60763e16			1.45477
$827$	1.16603e16	+	8.47172e15i	1.04817	+	0.761537i	0.971863	−	0.235547i	$-0.0756883\pi$
$827$	1.16603e16	+	8.47172e15i	1.04817	+	0.761537i	0.0763034	+	0.997085i	$0.475688\pi$
$828$	−2.98181e15	+	9.17706e15i	−0.266264	+	0.819477i
$829$	−1.24958e15	−	3.84580e15i	−0.110844	−	0.341143i	0.880213	−	0.474578i	$-0.157399\pi$
$829$	−1.24958e15	−	3.84580e15i	−0.110844	−	0.341143i	−0.991058	+	0.133435i	$0.957399\pi$
$830$	−7.93390e14	+	5.76432e14i	−0.0699129	+	0.0507947i
$831$	1.23301e16	−	8.95834e15i	1.07935	−	0.784191i
$832$	−1.16470e14	−	3.58457e14i	−0.0101283	−	0.0311716i
$833$	4.05040e14	−	1.24658e15i	0.0349905	−	0.107690i
$834$	−1.20592e16	−	8.76152e15i	−1.03492	−	0.751910i
$835$	1.52203e15			0.129762
$836$	1.65574e14	−	6.51031e14i	0.0140235	−	0.0551401i
$837$	−7.80001e15			−0.656305
$838$	6.19522e15	+	4.50109e15i	0.517862	+	0.376249i
$839$	3.55441e15	−	1.09394e16i	0.295173	−	0.908450i	−0.687990	−	0.725720i	$-0.741507\pi$
$839$	3.55441e15	−	1.09394e16i	0.295173	−	0.908450i	0.983163	−	0.182729i	$-0.0584932\pi$
$840$	4.02762e14	+	1.23957e15i	0.0332286	+	0.102267i
$841$	−1.04011e16	+	7.55682e15i	−0.852512	+	0.619386i
$842$	−7.05196e14	+	5.12355e14i	−0.0574240	+	0.0417210i
$843$	1.24067e15	+	3.81839e15i	0.100370	+	0.308907i
$844$	2.91573e15	−	8.97370e15i	0.234350	−	0.721254i
$845$	−1.55649e15	−	1.13086e15i	−0.124290	−	0.0903018i
$846$	1.68378e16			1.33582
$847$	−2.76239e15	+	1.48488e16i	−0.217734	+	1.17039i
$848$	−5.71740e14			−0.0447735
$849$	−1.40097e16	−	1.01786e16i	−1.09003	−	0.791950i
$850$	−7.46242e14	+	2.29670e15i	−0.0576867	+	0.177541i
$851$	7.31365e15	+	2.25091e16i	0.561723	+	1.72880i
$852$	1.40821e16	−	1.02313e16i	1.07461	−	0.780750i
$853$	−1.52159e16	+	1.10550e16i	−1.15366	+	0.838182i	−0.988963	−	0.148163i	$-0.952664\pi$
$853$	−1.52159e16	+	1.10550e16i	−1.15366	+	0.838182i	−0.164695	+	0.986345i	$0.552664\pi$
$854$	−6.53304e15	−	2.01066e16i	−0.492150	−	1.51468i
$855$	−1.08364e14	+	3.33510e14i	−0.00811093	+	0.0249629i
$856$	4.81038e15	+	3.49495e15i	0.357745	+	0.259917i
$857$	−1.18474e15			−0.0875441			−0.0437720	−	0.999042i	$-0.513938\pi$
$857$	−1.18474e15			−0.0875441			−0.0437720	+	0.999042i	$0.513938\pi$
$858$	−9.63897e14	+	3.79001e15i	−0.0707702	+	0.278266i
$859$	4.85534e15			0.354207			0.177104	−	0.984192i	$-0.443327\pi$
$859$	4.85534e15			0.354207			0.177104	+	0.984192i	$0.443327\pi$
$860$	−4.82748e12	−	3.50737e12i	−0.000349928	−	0.000254238i
$861$	3.92292e15	−	1.20735e16i	0.282548	−	0.869593i
$862$	−7.34540e14	−	2.26068e15i	−0.0525685	−	0.161789i
$863$	−3.85664e15	+	2.80201e15i	−0.274252	+	0.199256i	−0.716406	−	0.697683i	$-0.754214\pi$
$863$	−3.85664e15	+	2.80201e15i	−0.274252	+	0.199256i	0.442154	+	0.896939i	$0.354214\pi$
$864$	−1.24810e15	+	9.06801e14i	−0.0881912	+	0.0640747i
$865$	−1.14284e15	−	3.51731e15i	−0.0802412	−	0.246957i
$866$	1.59872e15	−	4.92035e15i	0.111538	−	0.343280i
$867$	1.67409e16	+	1.21630e16i	1.16058	+	0.843210i
$868$	9.19626e15			0.633509
$869$	−1.02213e16	+	8.49519e15i	−0.699680	+	0.581520i
$870$	−3.80602e15			−0.258890
$871$	−2.33366e14	−	1.69550e14i	−0.0157739	−	0.0114604i
$872$	−9.95071e14	+	3.06251e15i	−0.0668364	+	0.205701i
$873$	−8.84027e15	−	2.72076e16i	−0.590048	−	1.81598i
$874$	1.20963e15	−	8.78851e14i	0.0802308	−	0.0582911i
$875$	4.75569e15	−	3.45521e15i	0.313451	−	0.227735i
$876$	−5.04558e15	−	1.55287e16i	−0.330475	−	1.01710i
$877$	−1.78453e15	+	5.49221e15i	−0.116152	+	0.357478i	−0.992185	−	0.124772i	$-0.960180\pi$
$877$	−1.78453e15	+	5.49221e15i	−0.116152	+	0.357478i	0.876034	+	0.482250i	$0.160180\pi$
$878$	−1.15898e16	−	8.42045e15i	−0.749643	−	0.544647i
$879$	1.48960e16			0.957484
$880$	5.45941e14	+	3.44720e14i	0.0348731	+	0.0220197i
$881$	−1.99051e16			−1.26356			−0.631782	−	0.775146i	$-0.717676\pi$
$881$	−1.99051e16			−1.26356			−0.631782	+	0.775146i	$0.717676\pi$
$882$	−5.29011e15	−	3.84349e15i	−0.333724	−	0.242465i
$883$	6.84112e15	−	2.10548e16i	0.428887	−	1.31998i	−0.470335	−	0.882488i	$-0.655867\pi$
$883$	6.84112e15	−	2.10548e16i	0.428887	−	1.31998i	0.899223	−	0.437491i	$-0.144133\pi$
$884$	−1.76471e14	−	5.43123e14i	−0.0109948	−	0.0338385i
$885$	−5.76886e15	+	4.19132e15i	−0.357192	+	0.259515i
$886$	−4.61267e15	+	3.35130e15i	−0.283836	+	0.206219i
$887$	−7.34456e15	−	2.26042e16i	−0.449144	−	1.38232i	−0.877874	−	0.478891i	$-0.841039\pi$
$887$	−7.34456e15	−	2.26042e16i	−0.449144	−	1.38232i	0.428730	−	0.903433i	$-0.358961\pi$
$888$	−4.10581e15	+	1.26364e16i	−0.249533	+	0.767984i
$889$	4.71471e15	+	3.42544e15i	0.284771	+	0.206898i
$890$	−6.95774e14			−0.0417660
$891$	−7.41385e15	+	4.83424e14i	−0.442299	+	0.0288404i
$892$	1.85220e15			0.109820
$893$	−2.11077e15	−	1.53357e15i	−0.124382	−	0.0903690i
$894$	−1.01879e16	+	3.13552e16i	−0.596663	+	1.83634i
$895$	−5.45302e14	−	1.67827e15i	−0.0317403	−	0.0976865i
$896$	1.47152e15	−	1.06912e15i	0.0851281	−	0.0618492i
$897$	−7.04195e15	+	5.11627e15i	−0.404887	+	0.294168i
$898$	1.99874e15	+	6.15150e15i	0.114219	+	0.351529i
$899$	−8.29848e15	+	2.55401e16i	−0.471325	+	1.45059i
$900$	9.74646e15	+	7.08122e15i	0.550190	+	0.399737i
$901$	−8.66282e14			−0.0486041
$902$	−2.32840e15	−	5.84188e15i	−0.129844	−	0.325774i
$903$	1.74415e14			0.00966723
$904$	−1.02878e16	−	7.47452e15i	−0.566755	−	0.411772i
$905$	−1.09624e15	+	3.37387e15i	−0.0600256	+	0.184740i
$906$	3.81679e14	+	1.17469e15i	0.0207727	+	0.0639318i
$907$	−1.96632e15	+	1.42862e15i	−0.106369	+	0.0772815i	−0.639698	−	0.768626i	$-0.720941\pi$
$907$	−1.96632e15	+	1.42862e15i	−0.106369	+	0.0772815i	0.533329	+	0.845908i	$0.320941\pi$
$908$	−5.53641e15	+	4.02243e15i	−0.297684	+	0.216280i
$909$	−7.77821e15	−	2.39389e16i	−0.415698	−	1.27939i
$910$	−2.11822e14	+	6.51920e14i	−0.0112523	+	0.0346311i
$911$	1.51841e16	+	1.10319e16i	0.801749	+	0.582505i	0.911427	−	0.411462i	$-0.134982\pi$
$911$	1.51841e16	+	1.10319e16i	0.801749	+	0.582505i	−0.109678	+	0.993967i	$0.534982\pi$
$912$	8.39386e14			0.0440545
$913$	−5.25752e15	−	1.31910e16i	−0.274278	−	0.688157i
$914$	2.26157e16			1.17275
$915$	7.58644e15	+	5.51187e15i	0.391041	+	0.284108i
$916$	−2.91328e15	+	8.96615e15i	−0.149265	+	0.459389i
$917$	2.14818e15	+	6.61143e15i	0.109406	+	0.336716i
$918$	−1.89109e15	+	1.37396e15i	−0.0957365	+	0.0695566i
$919$	−1.83305e16	+	1.33179e16i	−0.922442	+	0.670193i	−0.944131	−	0.329572i	$-0.893096\pi$
$919$	−1.83305e16	+	1.33179e16i	−0.922442	+	0.670193i	0.0216889	+	0.999765i	$0.493096\pi$
$920$	4.44093e14	+	1.36678e15i	0.0222147	+	0.0683699i
$921$	−1.76170e16	+	5.42195e16i	−0.875999	+	2.69605i
$922$	−3.88476e15	−	2.82244e15i	−0.192019	−	0.139510i
$923$	9.15446e15			0.449804
$924$	−1.88325e16	+	1.22798e15i	−0.919838	+	0.0599786i
$925$	2.95491e16			1.43471
$926$	−5.60092e15	−	4.06931e15i	−0.270333	−	0.196408i
$927$	−2.82772e15	+	8.70281e15i	−0.135674	+	0.417562i
$928$	1.64133e15	+	5.05150e15i	0.0782857	+	0.240939i
$929$	1.51075e16	−	1.09763e16i	0.716321	−	0.520437i	−0.168886	−	0.985636i	$-0.554017\pi$
$929$	1.51075e16	−	1.09763e16i	0.716321	−	0.520437i	0.885207	+	0.465198i	$0.154017\pi$
$930$	−3.30002e15	+	2.39760e15i	−0.155546	+	0.113011i
$931$	3.13104e14	+	9.63636e14i	0.0146712	+	0.0451533i
$932$	−2.68463e15	+	8.26244e15i	−0.125054	+	0.384876i
$933$	8.40527e15	+	6.10679e15i	0.389227	+	0.282790i
$934$	8.22322e15			0.378560
$935$	8.27192e14	+	5.22309e14i	0.0378567	+	0.0239036i
$936$	−2.84894e15			−0.129618
$937$	1.77743e15	+	1.29138e15i	0.0803940	+	0.0584097i	0.627256	−	0.778813i	$-0.284178\pi$
$937$	1.77743e15	+	1.29138e15i	0.0803940	+	0.0584097i	−0.546862	+	0.837223i	$0.684178\pi$
$938$	4.30171e14	−	1.32393e15i	0.0193431	−	0.0595319i
$939$	1.87935e15	+	5.78406e15i	0.0840133	+	0.258566i
$940$	2.02879e15	−	1.47400e15i	0.0901640	−	0.0655080i
$941$	2.16215e16	−	1.57090e16i	0.955308	−	0.694072i	0.00325177	−	0.999995i	$-0.498965\pi$
$941$	2.16215e16	−	1.57090e16i	0.955308	−	0.694072i	0.952056	+	0.305923i	$0.0989649\pi$
$942$	−9.54499e14	−	2.93765e15i	−0.0419272	−	0.129039i
$943$	4.32549e15	−	1.33125e16i	0.188895	−	0.581360i
$944$	8.05069e15	+	5.84917e15i	0.349532	+	0.253950i
$945$	2.80576e15			0.121109
$946$	6.64483e13	−	5.52267e13i	0.00285156	−	0.00237000i
$947$	−1.35868e16			−0.579685			−0.289843	−	0.957074i	$-0.593603\pi$
$947$	−1.35868e16			−0.579685			−0.289843	+	0.957074i	$0.593603\pi$
$948$	−1.34356e16	−	9.76153e15i	−0.569916	−	0.414069i
$949$	2.65358e15	−	8.16689e15i	0.111910	−	0.344423i
$950$	−5.76861e14	−	1.77539e15i	−0.0241875	−	0.0744415i
$951$	−3.19718e16	+	2.32289e16i	−1.33283	+	0.968356i
$952$	2.22961e15	−	1.61990e15i	0.0924112	−	0.0671407i
$953$	−7.62845e15	−	2.34780e16i	−0.314359	−	0.967497i	−0.976018	−	0.217692i	$-0.930147\pi$
$953$	−7.62845e15	−	2.34780e16i	−0.314359	−	0.967497i	0.661659	−	0.749805i	$-0.269853\pi$
$954$	−1.33547e15	+	4.11015e15i	−0.0547164	+	0.168400i
$955$	3.64122e15	+	2.64550e15i	0.148330	+	0.107768i
$956$	−1.08257e16			−0.438467
$957$	1.35836e16	−	5.34101e16i	0.547014	−	2.15084i
$958$	−9.92037e15			−0.397208
$959$	−5.40692e15	−	3.92836e15i	−0.215252	−	0.156390i
$960$	−2.49310e14	+	7.67296e14i	−0.00986841	+	0.0303718i
$961$	1.04213e15	+	3.20734e15i	0.0410149	+	0.126231i
$962$	−5.65322e15	+	4.10731e15i	−0.221225	+	0.160729i
$963$	3.63607e16	−	2.64176e16i	1.41478	−	1.02789i
$964$	−3.29440e15	−	1.01391e16i	−0.127454	−	0.392262i
$965$	1.58591e15	−	4.88092e15i	0.0610067	−	0.187759i
$966$	−3.39837e16	−	2.46906e16i	−1.29986	−	0.944404i
$967$	−2.36244e16			−0.898494			−0.449247	−	0.893408i	$-0.648308\pi$
$967$	−2.36244e16			−0.898494			−0.449247	+	0.893408i	$0.648308\pi$
$968$	−6.78592e15	+	6.43093e15i	−0.256622	+	0.243197i
$969$	1.27181e15			0.0478235
$970$	−3.44695e15	−	2.50436e15i	−0.128882	−	0.0936380i
$971$	7.99700e15	−	2.46122e16i	0.297318	−	0.915052i	−0.685115	−	0.728435i	$-0.740248\pi$
$971$	7.99700e15	−	2.46122e16i	0.297318	−	0.915052i	0.982433	−	0.186616i	$-0.0597521\pi$
$972$	−5.44605e15	−	1.67612e16i	−0.201334	−	0.619642i
$973$	3.06068e16	−	2.22372e16i	1.12512	−	0.817445i
$974$	4.94929e15	−	3.59587e15i	0.180912	−	0.131441i
$975$	3.35822e15	+	1.03355e16i	0.122063	+	0.375671i
$976$	4.04395e15	−	1.24460e16i	0.146161	−	0.449838i
$977$	2.32330e16	+	1.68798e16i	0.834997	+	0.606661i	0.920969	−	0.389637i	$-0.127399\pi$
$977$	2.32330e16	+	1.68798e16i	0.834997	+	0.606661i	−0.0859714	+	0.996298i	$0.527399\pi$
$978$	4.76266e16			1.70210
$979$	2.48320e15	−	9.76385e15i	0.0882484	−	0.346989i
$980$	−9.73872e14			−0.0344158
$981$	1.96917e16	+	1.43068e16i	0.691994	+	0.502763i
$982$	7.12596e15	−	2.19315e16i	0.249018	−	0.766398i
$983$	8.16024e15	+	2.51146e16i	0.283569	+	0.872736i	0.986824	+	0.161798i	$0.0517293\pi$
$983$	8.16024e15	+	2.51146e16i	0.283569	+	0.872736i	−0.703255	+	0.710938i	$0.748271\pi$
$984$	6.35734e15	−	4.61888e15i	0.219686	−	0.159611i
$985$	−8.07212e14	+	5.86474e14i	−0.0277389	+	0.0201535i
$986$	2.48689e15	+	7.65388e15i	0.0849835	+	0.261552i
$987$	−2.26508e16	+	6.97119e16i	−0.769730	+	2.36899i
$988$	3.57142e14	+	2.59479e14i	0.0120692	+	0.00876877i
$989$	1.92314e14			0.00646295
$990$	3.75334e15	−	3.11949e15i	0.125437	−	0.104253i
$991$	2.06145e16			0.685123			0.342561	−	0.939495i	$-0.388706\pi$
$991$	2.06145e16			0.685123			0.342561	+	0.939495i	$0.388706\pi$
$992$	4.60532e15	+	3.34596e15i	0.152211	+	0.110588i
$993$	6.27031e15	−	1.92980e16i	0.206095	−	0.634296i
$994$	1.36519e16	+	4.20163e16i	0.446240	+	1.37338i
$995$	−1.03220e14	+	7.49939e13i	−0.00335535	+	0.00243781i
$996$	1.43549e16	−	1.04294e16i	0.464058	−	0.337158i
$997$	1.97098e15	+	6.06604e15i	0.0633663	+	0.195021i	0.977728	−	0.209878i	$-0.0673066\pi$
$997$	1.97098e15	+	6.06604e15i	0.0633663	+	0.195021i	−0.914361	+	0.404899i	$0.867307\pi$
$998$	9.15688e15	−	2.81820e16i	0.292772	−	0.901059i
$999$	2.31397e16	+	1.68120e16i	0.735781	+	0.534576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.12.c.a.15.5	yes	20
11.3	even	5	inner	22.12.c.a.3.5	✓	20
11.5	even	5		242.12.a.n.1.10		10
11.6	odd	10		242.12.a.m.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.12.c.a.3.5	✓	20	11.3	even	5	inner
22.12.c.a.15.5	yes	20	1.1	even	1	trivial
242.12.a.m.1.10		10	11.6	odd	10
242.12.a.n.1.10		10	11.5	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-25.8885 - 18.8091i) q^{2} +(201.415 - 619.892i) q^{3} +(316.433 + 973.882i) q^{4} +(932.620 - 677.588i) q^{5} +(-16874.0 + 12259.7i) q^{6} +(-16358.4 - 50346.1i) q^{7} +(10125.9 - 31164.2i) q^{8} +(-200383. - 145587. i) q^{9} +O(q^{10})\)	\(q+(-25.8885 - 18.8091i) q^{2} +(201.415 - 619.892i) q^{3} +(316.433 + 973.882i) q^{4} +(932.620 - 677.588i) q^{5} +(-16874.0 + 12259.7i) q^{6} +(-16358.4 - 50346.1i) q^{7} +(10125.9 - 31164.2i) q^{8} +(-200383. - 145587. i) q^{9} -36889.0 q^{10} +(131656. - 517666. i) q^{11} +667436. q^{12} +(283981. + 206324. i) q^{13} +(-523470. + 1.61108e6i) q^{14} +(-232188. - 714600. i) q^{15} +(-848316. + 616338. i) q^{16} +(-1.28534e6 + 933855. i) q^{17} +(2.44926e6 + 7.53805e6i) q^{18} +(379520. - 1.16804e6i) q^{19} +(955003. + 693851. i) q^{20} -3.45040e7 q^{21} +(-1.31452e7 + 1.09253e7i) q^{22} -3.80447e7 q^{23} +(-1.72789e7 - 1.25539e7i) q^{24} +(-1.46781e7 + 4.51744e7i) q^{25} +(-3.47107e6 - 1.06829e7i) q^{26} +(-3.71964e7 + 2.70248e7i) q^{27} +(4.38548e7 - 3.18624e7i) q^{28} +(4.89155e7 + 1.50546e8i) q^{29} +(-7.43001e6 + 2.28672e7i) q^{30} +(1.37249e8 + 9.97173e7i) q^{31} +3.35544e7 q^{32} +(-2.94380e8 - 1.85878e8i) q^{33} +5.08406e7 q^{34} +(-4.93701e7 - 3.58695e7i) q^{35} +(7.83764e7 - 2.41218e8i) q^{36} +(-1.92238e8 - 5.91649e8i) q^{37} +(-3.17951e7 + 2.31005e7i) q^{38} +(1.85096e8 - 1.34480e8i) q^{39} +(-1.16729e7 - 3.59256e7i) q^{40} +(-1.13695e8 + 3.49917e8i) q^{41} +(8.93257e8 + 6.48989e8i) q^{42} -5.05494e6 q^{43} +(5.45806e8 - 3.55896e7i) q^{44} -2.85529e8 q^{45} +(9.84923e8 + 7.15588e8i) q^{46} +(6.56469e8 - 2.02040e9i) q^{47} +(2.11199e8 + 6.50004e8i) q^{48} +(-6.67440e8 + 4.84923e8i) q^{49} +(1.22969e9 - 8.93419e8i) q^{50} +(3.20002e8 + 9.84865e8i) q^{51} +(-1.11074e8 + 3.41851e8i) q^{52} +(4.41119e8 + 3.20492e8i) q^{53} +1.47127e9 q^{54} +(-2.27980e8 - 5.71995e8i) q^{55} -1.73464e9 q^{56} +(-6.47618e8 - 4.70522e8i) q^{57} +(1.56530e9 - 4.81749e9i) q^{58} +(-2.93263e9 - 9.02572e9i) q^{59} +(6.22464e8 - 4.52247e8i) q^{60} +(-1.00967e10 + 7.33571e9i) q^{61} +(-1.67758e9 - 5.16307e9i) q^{62} +(-4.05177e9 + 1.24701e10i) q^{63} +(-8.68675e8 - 6.31130e8i) q^{64} +4.04649e8 q^{65} +(4.12485e9 + 1.03491e10i) q^{66} -8.21768e8 q^{67} +(-1.31619e9 - 9.56268e8i) q^{68} +(-7.66278e9 + 2.35836e10i) q^{69} +(6.03447e8 + 1.85722e9i) q^{70} +(2.10989e10 - 1.53292e10i) q^{71} +(-6.56614e9 + 4.77058e9i) q^{72} +(-7.55965e9 - 2.32662e10i) q^{73} +(-6.15163e9 + 1.89328e10i) q^{74} +(2.50469e10 + 1.81976e10i) q^{75} +1.25763e9 q^{76} +(-2.82162e10 + 1.83985e9i) q^{77} -7.32134e9 q^{78} +(-2.01302e10 - 1.46254e10i) q^{79} +(-3.73534e8 + 1.14962e9i) q^{80} +(-4.29821e9 - 1.32285e10i) q^{81} +(9.52502e9 - 6.92033e9i) q^{82} +(2.15075e10 - 1.56261e10i) q^{83} +(-1.09182e10 - 3.36028e10i) q^{84} +(-5.65966e8 + 1.74187e9i) q^{85} +(1.30865e8 + 9.50789e7i) q^{86} +1.03175e11 q^{87} +(-1.47995e10 - 9.34477e9i) q^{88} +1.88613e10 q^{89} +(7.39193e9 + 5.37055e9i) q^{90} +(5.74213e9 - 1.76725e10i) q^{91} +(-1.20386e10 - 3.70511e10i) q^{92} +(8.94580e10 - 6.49950e10i) q^{93} +(-5.49970e10 + 3.99577e10i) q^{94} +(-4.37504e8 - 1.34650e9i) q^{95} +(6.75837e9 - 2.08001e10i) q^{96} +(9.34412e10 + 6.78890e10i) q^{97} +2.64000e10 q^{98} +(-1.01747e11 + 8.45641e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9}+O(q^{10}) \) 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9	\( 20 q - 160 q^{2} + 56 q^{3} - 5120 q^{4} - 362 q^{5} - 3488 q^{6} - 167178 q^{7} - 163840 q^{8} + 206411 q^{9} - 354944 q^{10} - 449801 q^{11} + 108544 q^{12} + 3369596 q^{13} - 5349696 q^{14} + 12264628 q^{15} - 5242880 q^{16} + 1661262 q^{17} - 19177088 q^{18} + 49176291 q^{19} - 370688 q^{20} - 74218796 q^{21} - 5153632 q^{22} - 127653292 q^{23} - 3571712 q^{24} + 33758041 q^{25} - 99025728 q^{26} - 135657199 q^{27} + 156930048 q^{28} + 555960754 q^{29} + 392468096 q^{30} - 13977916 q^{31} + 671088640 q^{32} - 1768265081 q^{33} - 357119936 q^{34} + 584997860 q^{35} - 613666816 q^{36} - 161000626 q^{37} - 1456805888 q^{38} + 1145816470 q^{39} + 193593344 q^{40} + 772614122 q^{41} - 545038272 q^{42} + 3749722062 q^{43} - 50755584 q^{44} - 1321716548 q^{45} - 1394938624 q^{46} + 1924889212 q^{47} + 58720256 q^{48} + 822161735 q^{49} - 805012448 q^{50} + 5262939047 q^{51} - 3168823296 q^{52} + 1531782992 q^{53} + 295824512 q^{54} + 3851857218 q^{55} + 912654336 q^{56} - 17257259731 q^{57} + 17790744128 q^{58} - 16014164779 q^{59} - 3503935488 q^{60} + 7822116636 q^{61} + 6939975808 q^{62} - 79975953122 q^{63} - 5368709120 q^{64} + 73754374272 q^{65} - 3094015232 q^{66} - 22092583538 q^{67} + 1701132288 q^{68} + 43044165458 q^{69} - 5227997760 q^{70} + 23107180542 q^{71} + 6763675648 q^{72} + 55731754682 q^{73} - 5152020032 q^{74} - 37848703409 q^{75} - 7477467136 q^{76} - 52140560296 q^{77} - 110695592320 q^{78} + 43369591752 q^{79} + 6194987008 q^{80} - 19607689666 q^{81} + 6103740704 q^{82} + 105219370951 q^{83} + 55441248256 q^{84} - 14375063614 q^{85} - 53785859936 q^{86} - 216242949124 q^{87} + 14186872832 q^{88} - 227930374154 q^{89} + 138289668864 q^{90} + 236440118278 q^{91} + 109996521472 q^{92} + 215529449050 q^{93} + 24423998144 q^{94} + 242007717988 q^{95} + 1879048192 q^{96} - 200605898215 q^{97} + 128896464000 q^{98} - 634415317547 q^{99}+O(q^{100}) \) 20 * q - 160 * q^2 + 56 * q^3 - 5120 * q^4 - 362 * q^5 - 3488 * q^6 - 167178 * q^7 - 163840 * q^8 + 206411 * q^9 - 354944 * q^10 - 449801 * q^11 + 108544 * q^12 + 3369596 * q^13 - 5349696 * q^14 + 12264628 * q^15 - 5242880 * q^16 + 1661262 * q^17 - 19177088 * q^18 + 49176291 * q^19 - 370688 * q^20 - 74218796 * q^21 - 5153632 * q^22 - 127653292 * q^23 - 3571712 * q^24 + 33758041 * q^25 - 99025728 * q^26 - 135657199 * q^27 + 156930048 * q^28 + 555960754 * q^29 + 392468096 * q^30 - 13977916 * q^31 + 671088640 * q^32 - 1768265081 * q^33 - 357119936 * q^34 + 584997860 * q^35 - 613666816 * q^36 - 161000626 * q^37 - 1456805888 * q^38 + 1145816470 * q^39 + 193593344 * q^40 + 772614122 * q^41 - 545038272 * q^42 + 3749722062 * q^43 - 50755584 * q^44 - 1321716548 * q^45 - 1394938624 * q^46 + 1924889212 * q^47 + 58720256 * q^48 + 822161735 * q^49 - 805012448 * q^50 + 5262939047 * q^51 - 3168823296 * q^52 + 1531782992 * q^53 + 295824512 * q^54 + 3851857218 * q^55 + 912654336 * q^56 - 17257259731 * q^57 + 17790744128 * q^58 - 16014164779 * q^59 - 3503935488 * q^60 + 7822116636 * q^61 + 6939975808 * q^62 - 79975953122 * q^63 - 5368709120 * q^64 + 73754374272 * q^65 - 3094015232 * q^66 - 22092583538 * q^67 + 1701132288 * q^68 + 43044165458 * q^69 - 5227997760 * q^70 + 23107180542 * q^71 + 6763675648 * q^72 + 55731754682 * q^73 - 5152020032 * q^74 - 37848703409 * q^75 - 7477467136 * q^76 - 52140560296 * q^77 - 110695592320 * q^78 + 43369591752 * q^79 + 6194987008 * q^80 - 19607689666 * q^81 + 6103740704 * q^82 + 105219370951 * q^83 + 55441248256 * q^84 - 14375063614 * q^85 - 53785859936 * q^86 - 216242949124 * q^87 + 14186872832 * q^88 - 227930374154 * q^89 + 138289668864 * q^90 + 236440118278 * q^91 + 109996521472 * q^92 + 215529449050 * q^93 + 24423998144 * q^94 + 242007717988 * q^95 + 1879048192 * q^96 - 200605898215 * q^97 + 128896464000 * q^98 - 634415317547 * q^99

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